193. Find z such that -9/4 - 9/4*z**4 + 9/2*z**2 + 3/4*z**x - 3/2*z**3 + 3/4*z = 0.
-1, 1, 3
Suppose 5*h - 6 = 14. What is u in 136*u**2 + 120*u + 491*u**3 + 27*u**h + 17*u**2 + 3*u**5 - 398*u**3 + 36 = 0?
-3, -2, -1
Let p(m) be the first derivative of -5*m**4/4 + 5*m**3/3 + 85*m**2/2 + 75*m - 1430. Factor p(y).
-5*(y - 5)*(y + 1)*(y + 3)
Let n(v) = v**3 + 8*v**2 - 13*v + 41. Let p be n(-9). Factor -42*f + p*f - 32*f - f**2.
-f*(f - 3)
Let v(k) be the first derivative of -k**4/38 + 56*k**3/57 + 220*k**2/19 - 15488*k/19 + 3272. Factor v(i).
-2*(i - 22)**2*(i + 16)/19
Let b(f) = 4*f**2 - 61*f - 2392. Let v be b(-18). Determine t so that -1 - 33/2*t**3 - 45/2*t**4 + 19/2*t**v + 5/2*t = 0.
-1, -2/5, 1/3
Find s such that -40*s**4 - 90*s + 267*s + 37*s**4 - 177*s**3 + 3*s**2 = 0.
-59, -1, 0, 1
Let d(t) be the first derivative of 3*t**4/10 - 82*t**3/15 + 26*t**2/5 + 1628. Factor d(y).
2*y*(y - 13)*(3*y - 2)/5
Suppose -291*b + 2616 = 391*b + 570. Let 24/7*r**2 - 40/7 - 12/7*r - 4/7*r**b = 0. Calculate r.
-1, 2, 5
Let d(x) be the first derivative of -2*x**6/15 - 4*x**5/5 + 7*x**4/3 + 20*x**3/3 + 92*x + 180. Let k(l) be the first derivative of d(l). Factor k(o).
-4*o*(o - 2)*(o + 1)*(o + 5)
Let n(r) be the third derivative of r**5/20 + 617*r**4/24 + 205*r**3/3 + 8301*r**2. Determine m, given that n(m) = 0.
-205, -2/3
Let f(d) be the third derivative of 0*d - 1/40*d**5 + 3/8*d**4 + 1/140*d**7 + 1/224*d**8 + 0*d**3 - 27 - 7/80*d**6 + d**2. Determine h, given that f(h) = 0.
-3, -1, 0, 1, 2
Let j(o) = o**2 - 67 + 40*o - 6*o**2 - 208. Let h(y) = y + 1. Suppose 116 = -4*n - 2*s, 3*n + 5*s + 20 = 2*n. Let c(l) = n*h(l) - j(l). Factor c(a).
5*(a - 7)**2
Solve -10/9*d**5 - 16/9*d**2 - 20/3*d**3 - 6*d**4 + 0*d + 0 = 0.
-4, -1, -2/5, 0
Let n be (2 - -1)*1 + 2. Let c be (-2)/7 - 44/(-231)*n. Factor -10/3 - c*r**2 - 4*r.
-2*(r + 1)*(r + 5)/3
Let s be (-8)/(-36) - (-128)/72. Suppose 2 = -2*a, -s*c + 8*a = 3*a - 9. Solve -4/3*j**c + 1/6*j**3 - 1 + 13/6*j = 0 for j.
1, 6
Let n(h) be the second derivative of -1/36*h**4 - 8/9*h**3 - 5/2*h**2 - 59*h + 0. Factor n(x).
-(x + 1)*(x + 15)/3
Let l(w) be the first derivative of -w**6/840 - w**5/30 - 7*w**4/24 - 57*w**2/2 + 127. Let k(h) be the second derivative of l(h). Let k(j) = 0. What is j?
-7, 0
Let x(n) be the third derivative of 0*n**6 + 0*n**3 + 0 + 0*n**4 - 1/84*n**7 + 0*n**5 - 185*n - 5/672*n**8 - n**2. Factor x(q).
-5*q**4*(q + 1)/2
Let g(k) be the third derivative of k**8/8400 + k**7/700 - k**6/120 + k**5/75 - 29*k**3/3 + 61*k**2. Let d(f) be the first derivative of g(f). Factor d(p).
p*(p - 1)**2*(p + 8)/5
Factor 120 - 257 + 125 - 46*h + 315*h**2 - 578*h.
3*(h - 2)*(105*h + 2)
Let i = 2/385 + 1151/770. Suppose 2*f - 15 = -9. Factor 1/2*v**f - 1/2*v - 3/2*v**2 + i.
(v - 3)*(v - 1)*(v + 1)/2
Suppose 2*z + 2*l + 5 = 17, 0 = -z - 2*l + 9. Suppose -7*k + 15 = -2*k. Factor 6*a**z - 15*a**2 - k*a**4 + 15*a**2.
-3*a**3*(a - 2)
Let g(r) = r**3 + 36*r**2 + 36*r + 44. Let a be g(-35). Find i such that -828*i**3 + 57*i + 76*i**2 - a*i - 80 + 4*i**4 + 780*i**3 = 0.
-1, 1, 2, 10
Let v(y) be the first derivative of -1/9*y**6 + 0*y - 139 + 0*y**3 + 4/15*y**5 + 0*y**2 + 0*y**4. Factor v(h).
-2*h**4*(h - 2)/3
Let p(z) be the second derivative of 3*z**5/100 + 7*z**4/10 - 19*z**3/2 + 3*z - 47. Suppose p(x) = 0. Calculate x.
-19, 0, 5
Let g be (-31 - -19)/192*-20. Solve -2*j + g*j**4 + 1/4*j**5 - j**2 + 0 + 3/2*j**3 = 0.
-2, 0, 1
Find s, given that -28*s**3 + 79/3*s - 74/3*s**2 + 5/3*s**5 + 0 + 74/3*s**4 = 0.
-79/5, -1, 0, 1
Let m(u) be the third derivative of -1/90*u**5 + 2/27*u**3 + 0*u - 1/36*u**4 + 1/270*u**6 + 0 + 33*u**2. Find l such that m(l) = 0.
-1, 1/2, 2
Let w be -5*(((-24)/4)/(-6))/(-1). Suppose 3*k - 14 + w = 0. Solve -1/3*t**k + 0*t**2 + t + 2/3 = 0.
-1, 2
Let w(z) = 6*z**2 - 7960*z. Let x(o) = -4*o**2 + 5309*o. Let j(h) = -5*w(h) - 8*x(h). Solve j(l) = 0 for l.
0, 1336
Let w(f) be the third derivative of 2*f**7/105 - 67*f**6/5 - 72*f**2 + 19. Factor w(m).
4*m**3*(m - 402)
Let v(a) be the first derivative of a**5/15 + a**4/2 + 4*a**3/3 + 26*a**2 + 61. Let p(z) be the second derivative of v(z). Factor p(u).
4*(u + 1)*(u + 2)
Determine q, given that -20*q**4 + 662692*q**5 - 662694*q**5 - 6*q**2 + 114*q**2 - 144*q + 58*q**3 = 0.
-12, -2, 0, 1, 3
Let m(v) be the first derivative of 3*v**4/4 - 14*v**3 - 3*v**2/2 + 42*v - 416. Factor m(t).
3*(t - 14)*(t - 1)*(t + 1)
Factor 58/7*h + 156/7 + 2/7*h**2.
2*(h + 3)*(h + 26)/7
Factor 88/5*n**2 + 14/5*n**3 - 108/5 - 354/5*n.
2*(n - 3)*(n + 9)*(7*n + 2)/5
What is t in -8796*t**5 - 20*t + 17615*t**5 + 8*t**2 - 8815*t**5 - 16*t**4 + 8 + 4*t**3 + 12*t**3 = 0?
-1, 1, 2
Solve 88/7*r**2 - 76/7*r**3 - 16/7*r + 18/7*r**4 + 0 = 0 for r.
0, 2/9, 2
Let f(v) = -v + 8*v**3 - 13*v**3 - 6*v**2 + 18*v**2 + 6*v**3 - 9. Let p be f(-12). Factor 17*i**2 - i**p - 5*i + i**3 - 21*i**2 - i**3 - 2.
-(i + 1)**2*(i + 2)
Let n(x) be the first derivative of x**3/8 - 102*x**2 + 813*x/2 + 6170. Determine s so that n(s) = 0.
2, 542
Let t(y) be the first derivative of 0*y - 1/40*y**6 - 30 + 0*y**3 - 9*y**2 + 1/5*y**5 - 3/8*y**4. Let i(h) be the second derivative of t(h). Factor i(c).
-3*c*(c - 3)*(c - 1)
Let h be (1 - -47)*((-430)/(-160))/43. Let -1/5*q**4 + 17/5*q**2 + 36/5*q + 0*q**h + 4 = 0. Calculate q.
-2, -1, 5
Let t = 3077/8241 + -110/2747. Let 10/3*m**2 + 0*m**3 - 2 - 4/3*m**4 + t*m - 1/3*m**5 = 0. What is m?
-3, -2, -1, 1
Let l(h) be the first derivative of -8*h**2 + 5*h**4 + 21 - 12/5*h**5 + 0*h - 2/3*h**6 + 4*h**3. Let l(r) = 0. What is r?
-4, -1, 0, 1
Let f(t) be the third derivative of 0*t**3 + t**2 + 1/14*t**4 - 50*t + 0 - 1/7*t**5 - 11/280*t**6. Factor f(v).
-3*v*(v + 2)*(11*v - 2)/7
Let n(u) be the first derivative of 8*u**4 + 644*u**3/15 + 328*u**2/5 + 16*u/5 + 1909. Find v such that n(v) = 0.
-2, -1/40
Let g(h) be the first derivative of h**4/8 + 271*h**3/6 - 274*h**2 + 550*h - 7061. Find c, given that g(c) = 0.
-275, 2
Let a(u) = -3*u**2 - 15*u + 16. Let d be a(-5). Factor -16 - 8 - 537*f + 581*f - 4*f**3 - d*f**2.
-4*(f - 1)**2*(f + 6)
Let n(j) be the second derivative of 2*j**6/75 - j**5/25 - 5*j**4/3 + 10*j**3/3 + 458*j. Factor n(p).
4*p*(p - 5)*(p - 1)*(p + 5)/5
Let k = 10258/51165 + -5/10233. Factor 0*d**2 - d**4 + 0 + 0*d + 0*d**3 - k*d**5.
-d**4*(d + 5)/5
Let x be -22*(-5)/20*260/143. Let j(d) be the third derivative of 0*d + 0 - 1/18*d**4 - x*d**2 - 1/3*d**3 + 1/90*d**5. Factor j(l).
2*(l - 3)*(l + 1)/3
Suppose -3599*w + 2984 = -3191*w - 6180 + 596. Determine d, given that -33*d**4 + 0 + w*d**5 - 198/7*d**3 + 156/7*d**2 - 24/7*d = 0.
-1, 0, 2/7, 2
Suppose -4*s + 167 = -3*z, 0*s - 78 = -2*s - 4*z. Suppose 0 = 3*r - 4*d - 23 - 97, -5*d - 159 = -4*r. Factor -s*v**2 + 14 + 30*v + r*v**2 - 39.
-5*(v - 5)*(v - 1)
Factor -560 - 120*h**2 - 19*h + 131*h**2 - 4*h**3 + 2*h**3 - 129*h + 51*h**2.
-2*(h - 28)*(h - 5)*(h + 2)
Let a(i) = -6*i**2 + 60*i + 168. Let q(z) = -3*z**2 - z + 2. Let v(n) = a(n) - 3*q(n). Factor v(x).
3*(x + 3)*(x + 18)
Let t be -17 + (-91)/((-2912)/640). Factor 7/2*g - 3/2*g**2 + t.
-(g - 3)*(3*g + 2)/2
Let c = 442/189 + -4484/2079. Let c*n - 6/11*n**2 + 48/11 = 0. What is n?
-8/3, 3
Let m be 3 - (-5 - (2 + (-4 - 2))). Solve -54*w + 16*w**2 + 126*w - 56*w + m*w**3 = 0 for w.
-2, 0
Let y(m) be the second derivative of 2*m + 82 - 2*m**2 + 29/45*m**3 + 1/90*m**4. Let y(a) = 0. Calculate a.
-30, 1
Let k(p) = 321*p - p**3 - 23 - 992*p + 339*p + 362*p. Let u be k(5). What is y in 1/9*y**4 - u + 1/3*y + 13/9*y**2 - 7/9*y**3 = 0?
-1, 2, 3
Let i be (25 - 19)*(-1 + (-25)/(-3)). Factor -8*u**2 + 52*u**2 - 23*u**3 + 8*u**4 - i + 60*u - 21*u**3 + 8.
4*(u - 3)**2*(u + 1)*(2*u - 1)
Suppose -6 - 19 = 5*x, -x = -4*n + 65. Determine b so that 228*b**2 - 116*b**2 + 3*b - 113*b**2 + 3 + n = 0.
-3, 6
Suppose -4*n = d - 12, -58*n + 9 = -4*d - 55*n. Let b(y) be the third derivative of -17*y**2 + 0 + 0*y + 1/27*y**4 + d*y**3 + 1/135*y**5. Factor b(x).
4*x*(x + 2)/9
Let j(n) be the third derivative of n**9/332640 - n**8/7920 - 4*n**7/3465 + 31*n**5/20 + 160*n**2. Let d(u) be the third derivative of j(u). Factor d(p).
2*p*(p - 16)*(p + 2)/11
Let y(c) be the third derivative of 1/480*c**6 - c**2 - 13 + 0*c**3 + 1/240*c**5 - 1/8*c**4 + 0*c. Factor y(q).
q*(q - 3)*(q + 4)/4
Let x(s) = 40*s**3 - 64*s**2 + 1