/78. Solve 12/13*t + f*t**2 + 18/13 = 0.
-3
Find n, given that -13 + 10*n + 0*n + 38 + n**2 = 0.
-5
Let q = 2036/9 - 226. Factor 4/9*s**2 + q*s + 0.
2*s*(2*s + 1)/9
Let k(l) be the first derivative of -2*l**5/5 - l**4/2 + 7. What is t in k(t) = 0?
-1, 0
Let j(v) be the third derivative of -v**5/60 - v**3/6 - 10*v**2. Let z(g) = -3*g + 4*g**2 + 5 + 3*g - g**3. Let s(h) = 5*j(h) + z(h). Factor s(q).
-q**2*(q + 1)
Let n be (434/(-8))/(-7) + -2. Let b(y) be the first derivative of -1 - 2/3*y**2 - n*y**4 - 28/9*y**3 + 0*y - 14/3*y**5 - 25/18*y**6. Let b(j) = 0. Calculate j.
-1, -2/5, 0
Let x = -4 + 5. Let a be -1 + 0 + x + 3. Solve 0*i**a + 0*i - 2/5*i**4 - 2/5 + 4/5*i**2 = 0 for i.
-1, 1
Let o(n) = 29*n + 5. Let y be o(0). Suppose 0 - 6/7*h**4 + 2/7*h**y + 6/7*h**3 - 2/7*h**2 + 0*h = 0. What is h?
0, 1
Let b be (-1 - (-13)/11)/((-18)/(-66)). Factor 0 + b*i + 1/3*i**2.
i*(i + 2)/3
Determine f, given that 1/2*f**2 + 0*f + 1/2*f**4 + 0 + f**3 = 0.
-1, 0
Let r(g) = g + 2. Let w be r(4). Factor 6/7*f + w*f**3 + 0 + 33/7*f**2.
3*f*(2*f + 1)*(7*f + 2)/7
Find g, given that -2/9*g + 4/9*g**3 + 0 - 2/9*g**2 = 0.
-1/2, 0, 1
Let t(h) be the third derivative of h**9/7560 - h**8/1400 + h**7/700 - h**6/900 - h**3/2 + 6*h**2. Let j(c) be the first derivative of t(c). Factor j(a).
2*a**2*(a - 1)**3/5
Let d(b) = -b**3 + 5*b**2 + 5*b - 1. Let l(c) = 3*c**3 - 11*c**2 - 11*c + 3. Let a(z) = -5*d(z) - 2*l(z). Factor a(m).
-(m + 1)**3
Let i(r) = -r**2 - 16*r + 17. Let a be i(1). Factor -1/3*m**2 + a - 1/3*m.
-m*(m + 1)/3
Let q(f) be the third derivative of f**10/756000 + f**9/151200 + f**8/100800 + f**5/20 + 3*f**2. Let w(u) be the third derivative of q(u). Factor w(l).
l**2*(l + 1)**2/5
Let b = -172 - -345/2. What is i in -3/2*i - 1 - b*i**2 = 0?
-2, -1
Let h be (-1)/((12/(-9))/(-4)). Let v = h - -6. Determine w so that -6*w - 4*w**3 + 2*w**v + 2*w + 6*w**2 = 0.
0, 1, 2
Let t(a) = -a**3 - 5*a**2 + 5*a - 4. Let r be t(-6). Factor -6*v + 31*v + 10*v + 14*v**r + 8 - 3*v.
2*(v + 2)*(7*v + 2)
Let c(q) be the first derivative of 3*q**4/4 + 27*q**3 + 252*q**2 - 588*q + 41. Let c(t) = 0. What is t?
-14, 1
Suppose -b - 14 = -z, 2*z - 3*b + 2*b = 24. Let m(r) = -2*r + 23. Let p be m(z). Determine y so that -2*y + 2*y**p - 2/3 + 2/3*y**2 = 0.
-1, -1/3, 1
Let x(g) be the first derivative of 2*g**3/33 + g**2/11 - 1. What is k in x(k) = 0?
-1, 0
Let d(i) be the first derivative of -i**6/630 - i**5/420 + 4*i**3/3 + 2. Let k(j) be the third derivative of d(j). Factor k(n).
-2*n*(2*n + 1)/7
Suppose -14/3*h**3 + 0*h + 0 - 2*h**2 - 2/3*h**5 - 10/3*h**4 = 0. Calculate h.
-3, -1, 0
Let a = 94747/795 - -67/159. Let s = 120 - a. Suppose -2/5*d + 0 + 0*d**2 + s*d**3 = 0. Calculate d.
-1, 0, 1
Let x(g) be the third derivative of -1/36*g**4 + 4*g**2 + 0*g - 1/270*g**5 + 0 - 2/27*g**3. Factor x(z).
-2*(z + 1)*(z + 2)/9
Let a be 21/6 - 5/(-10). What is x in 213*x**a + 7*x**3 - 6*x - 84*x**5 + 0*x**2 - 187*x**3 + 50*x**2 + 7*x**2 = 0?
0, 1/4, 2/7, 1
Let r be (-5)/20 + (-1)/(-4). Let c(o) be the first derivative of 2 + r*o + 0*o**2 + 1/12*o**3 - 1/24*o**6 + 1/16*o**4 - 1/20*o**5. Factor c(l).
-l**2*(l - 1)*(l + 1)**2/4
Let q(m) be the third derivative of m**6/120 + m**5/4 - 5*m**4/8 + 3*m**3 + 13*m**2. Let y be q(-16). Factor 0 + o + 1/2*o**y - 3/2*o**3.
-o*(o - 1)*(3*o + 2)/2
Suppose i + 9 = q, 3*q - i = i + 27. Let b = q + -6. Factor 1/3*l**2 + 0 + 1/3*l**b + 0*l - 1/3*l**4 - 1/3*l**5.
-l**2*(l - 1)*(l + 1)**2/3
Let t(w) = w**3 - 5*w**2 + 2. Let c be t(5). Factor -8*f**2 - 11 + 3 + 6*f**c + 8*f.
-2*(f - 2)**2
Factor -160/3 - 5/6*n**2 - 40/3*n.
-5*(n + 8)**2/6
Let h = -7 + 12. Suppose -1 = -l - h. Let w(m) = 6*m**2 - 4*m + 2. Let o(u) = u**2. Let n(g) = l*o(g) + w(g). Factor n(k).
2*(k - 1)**2
Let k(d) be the first derivative of d**4/20 + d**3/5 + 3*d**2/10 + d/5 - 19. Find l, given that k(l) = 0.
-1
Let l(w) = -4*w + 12. Let j be l(3). Factor -2/5*p**2 + 2/5*p + j - 2/5*p**3 + 2/5*p**4.
2*p*(p - 1)**2*(p + 1)/5
Suppose 0 = -3*w + 12, h + 5*w = w + 20. Factor -5*p**2 - 7*p**2 + 0*p**2 + h*p - 4*p**2.
-4*p*(4*p - 1)
Let u(t) = -2*t**3 - 5*t**2 + t + 3. Suppose 2*d + 5 = -3*d. Let z(g) = -13 - 10 + 24 - g**3 - g**2. Let i(c) = d*u(c) + 3*z(c). Find w such that i(w) = 0.
0, 1
Suppose d - 2*d = 0. Let h(l) be the second derivative of -1/2*l**2 + d - 1/3*l**3 - 1/12*l**4 - 2*l. Factor h(s).
-(s + 1)**2
Factor 7*n + 0*n**2 - 3*n**2 - 4*n**2 - 5*n.
-n*(7*n - 2)
Suppose -2*b + 8 = 2*b, -8 = -5*q + b. Let z(a) be the third derivative of 1/60*a**4 + 2*a**q + 0 + 0*a**3 + 0*a**5 + 0*a - 1/300*a**6. Factor z(p).
-2*p*(p - 1)*(p + 1)/5
Let u(p) be the first derivative of 7*p**6/2 - 36*p**5/5 + 9*p**4/4 + 2*p**3 + 22. What is x in u(x) = 0?
-2/7, 0, 1
Suppose -4*o + o = -15. Suppose o = -0*d + d. Factor 43*h + 81*h**5 - 2 - 32*h**d - 2 - 145*h**2 - 3*h + 235*h**3 - 175*h**4.
(h - 1)**3*(7*h - 2)**2
Factor 0*a**2 + 0*a + 33/5*a**4 + 0 + 2/5*a**3.
a**3*(33*a + 2)/5
Let n(i) be the third derivative of -i**8/672 + i**7/210 - i**6/240 - 5*i**2. Factor n(c).
-c**3*(c - 1)**2/2
Let a be (5 - 9/10) + -4. Let z(v) be the first derivative of -1/20*v**4 + 0*v + 2 + 0*v**3 + a*v**2. Factor z(g).
-g*(g - 1)*(g + 1)/5
Let a(c) be the first derivative of -3*c**4/4 + c**3 + 3*c**2/2 - 3*c + 4. Let z(j) = 6*j**3 - 6*j**2 - 6*j + 6. Let v(n) = 9*a(n) + 4*z(n). Factor v(w).
-3*(w - 1)**2*(w + 1)
Factor 3*a**2 + 12*a - 3 + 1 - 1 - 12.
3*(a - 1)*(a + 5)
Solve 25 + 0*a - 7*a**2 - 10*a + 3*a**2 + 5*a**2 = 0 for a.
5
Let j(c) = 4*c**3 + 5*c**2 + 3. Let w be (-6)/(((-30)/4)/5). Let f(d) = 9*d**3 + 8 + 0 + w*d**3 + 14*d**2. Let a(r) = 3*f(r) - 8*j(r). Factor a(l).
l**2*(7*l + 2)
Let q(i) = 81*i**2 - 96*i - 177. Let l(a) = -5*a**2 + 6*a + 11. Let w(n) = 33*l(n) + 2*q(n). What is c in w(c) = 0?
-1, 3
Let h = -27 + 12. Let n be (-12)/(-18) + 4/h. Factor 0 - 2/5*l**3 + 0*l + n*l**2.
-2*l**2*(l - 1)/5
Let z(n) = -n**2 + n + 9. Let o be 52/(-9) + 10/(-45). Let x(t) = t**2 - t - 8. Let y(h) = o*z(h) - 7*x(h). Factor y(f).
-(f - 2)*(f + 1)
Let a be 0*((-16)/(-6) - 3). Let w(y) = -y**3 + 5*y**2 + 6*y + 2. Let n be w(6). Factor a - 2*g**n + 0*g**2 + 2.
-2*(g - 1)*(g + 1)
Let b(a) be the second derivative of 7*a**5/5 + 10*a**4 + 16*a**3/3 - 10*a + 2. Find f such that b(f) = 0.
-4, -2/7, 0
Factor -4/3*r + 1/3 + 2*r**2 - 4/3*r**3 + 1/3*r**4.
(r - 1)**4/3
Suppose s - 3*j - 18 = 0, 6*j - 5*j = -2*s + 8. Factor 3/2*d**4 + 9*d**2 - s*d - 6*d**3 + 3/2.
3*(d - 1)**4/2
Let t(u) be the third derivative of u**8/2184 - u**6/390 + u**4/156 + 10*u**2. Factor t(g).
2*g*(g - 1)**2*(g + 1)**2/13
Let j = -76/45 + 32/15. Let r be (-2)/(-8*1) - (-88)/32. Find c, given that 2/3*c**5 - 4/3*c**r - 2/9 + j*c**2 - 2/9*c**4 + 2/3*c = 0.
-1, 1/3, 1
Let a = -1/7415 + -1149283/311430. Let w = -17/6 - a. Factor 0 + w*b**3 + 4/7*b - 2/7*b**4 + 10/7*b**2 - 2/7*b**5.
-2*b*(b - 2)*(b + 1)**3/7
Let d(a) be the third derivative of -a**8/47040 + a**7/5880 + 7*a**5/60 - 7*a**2. Let r(v) be the third derivative of d(v). Suppose r(l) = 0. What is l?
0, 2
Let k be 2/2 + 2 + -1. Factor -2/5*i**k + 0 + 1/5*i + 1/5*i**3.
i*(i - 1)**2/5
Let m(u) be the second derivative of 3*u**7/70 - u**6/10 + u**5/20 - u**2 - 3*u. Let q(z) be the first derivative of m(z). Let q(l) = 0. Calculate l.
0, 1/3, 1
Let n be 7*(0 + -1) + -1. Let v be (12/15)/(n/(-40)). Factor -1/4 + 1/2*s**3 - 1/2*s + 0*s**2 + 1/4*s**v.
(s - 1)*(s + 1)**3/4
Let w = -901/7 - -129. Find d such that -2/7*d + 2/7 - 4/7*d**2 - w*d**5 + 4/7*d**3 + 2/7*d**4 = 0.
-1, 1
Let c(b) = -2*b - 17. Let z be (1 + 28/12)*-3. Let v be c(z). Factor 11/5*m**2 - v*m**3 + 0 - 2/5*m.
-m*(3*m - 1)*(5*m - 2)/5
Let a(b) be the third derivative of 0*b - 1/105*b**7 + b**2 + 0*b**6 + 0 + 0*b**3 + 1/6*b**4 + 1/10*b**5. Factor a(f).
-2*f*(f - 2)*(f + 1)**2
Let u(w) be the second derivative of 0 + 1/6*w**4 + 2/3*w**3 + 0*w**2 + w. Factor u(x).
2*x*(x + 2)
Let y(u) be the second derivative of -2*u + 1/12*u**3 + 0*u**2 - 1/48*u**4 + 0. Factor y(m).
-m*(m - 2)/4
Let a(u) be the third derivative of u**6/1020 - u**4/68 + 2*u**3/51 + 20*u**2. What is t in a(t) = 0?
-2, 1
Let v(o) be the third derivative of -o**7/42 + o**6/24 + o**5/12 - 5*o**4/24 - 13*o**2. Suppose v(b) = 0. What is b?
-1, 0, 1
Let o(f) be the third derivative of f**5/12 - 5*f**4/6 + 10*f**3/3 + 1