20. Let u = 51/56 - 5/8. Solve -2/7*b**z - 6/7*b**2 - u - 6/7*b = 0 for b.
-1
Let j(b) = -2*b**3 + 87*b**2 - 162*b + 80. Let d(c) = 5*c**3 - 175*c**2 + 325*c - 160. Let z(h) = 3*d(h) + 5*j(h). Find p such that z(p) = 0.
1, 16
Let z = -4 + 7. Determine c, given that c**2 + 5*c**2 - z*c**3 - 12*c**3 = 0.
0, 2/5
Let n be ((-3)/(-20))/(105/14). Let c(l) be the second derivative of n*l**5 - 2/75*l**6 + 0*l**3 + l + 0 + 0*l**2 + 0*l**4. Find r, given that c(r) = 0.
0, 1/2
Let b be ((-6)/((-48)/20))/(2/4). Let z(v) be the third derivative of 0*v**3 + 0 + 0*v**b - 4*v**2 + 0*v**4 + 1/720*v**6 + 0*v. Determine m so that z(m) = 0.
0
Let x be 1/5 - 313/(-135). Let n = 4/27 + x. Determine t so that 70/3*t**5 + 0 + n*t - 6*t**3 - 92/3*t**4 + 32/3*t**2 = 0.
-2/5, -2/7, 0, 1
Let l(n) be the second derivative of n**7/140 - n**5/15 - 7*n**4/12 - n. Let b(x) be the third derivative of l(x). Solve b(u) = 0.
-2/3, 2/3
Suppose -2*z = -4*l - 34, -3*z - 16 = -4*l - 57. Factor -b**2 + z*b - 4 - 7*b - 4*b.
-(b + 2)**2
Let x(h) = -6*h**4 + 3*h**3 - 3*h - 4. Let f(t) = 7*t**4 - 4*t**3 + 4*t + 5. Let y be -1 + 0 + -2 - 2. Let k(j) = y*f(j) - 6*x(j). Solve k(v) = 0.
-1, 1
Let b be (5/(-25))/((-2)/10). Let z(n) be the first derivative of -b + 1/22*n**4 + 0*n**2 + 0*n + 2/55*n**5 - 1/33*n**6 - 2/33*n**3. Solve z(v) = 0.
-1, 0, 1
Let o(d) be the third derivative of 5*d**6/24 + d**5/4 - 5*d**4/12 + 7*d**2. Solve o(w) = 0 for w.
-1, 0, 2/5
Let m = 39 - 39. Let f(q) be the second derivative of 1/18*q**4 + 1/3*q**3 + m + q + 2/3*q**2. Determine r so that f(r) = 0.
-2, -1
Let g(a) be the first derivative of 1 - 1/3*a**3 + 0*a**2 + 0*a - 3/4*a**4. Factor g(b).
-b**2*(3*b + 1)
Let v(h) be the third derivative of -h**6/96 + 10*h**2 + 3. Suppose v(t) = 0. Calculate t.
0
Let b = -53 - -109/2. Factor m**2 + 0 - 1/2*m**5 + 0*m + 0*m**4 + b*m**3.
-m**2*(m - 2)*(m + 1)**2/2
Factor 1/3*l**4 + 13/3*l**2 - 4*l + 4/3 - 2*l**3.
(l - 2)**2*(l - 1)**2/3
Let -3/5 + 3/5*x**2 - 3/5*x**3 + 3/5*x = 0. What is x?
-1, 1
Let o(v) be the third derivative of 3*v**5/50 - 3*v**4/20 + 2*v**3/15 + v**2. Determine w so that o(w) = 0.
1/3, 2/3
Let a be 4/8*(-156)/(-91). Factor 12/7 - 12/7*w - 9/7*w**2 + a*w**3 + 3/7*w**4.
3*(w - 1)**2*(w + 2)**2/7
Suppose -2/5*r**3 - 2/5*r**4 + 0 + 2/5*r + 2/5*r**2 = 0. Calculate r.
-1, 0, 1
Let r(o) = 15*o**3 + 36*o**2 + 20*o - 1. Let c(b) = -b. Let j be c(-2). Let x(a) = 5*a**3 + 12*a**2 + 7*a. Let q(d) = j*r(d) - 7*x(d). Factor q(i).
-(i + 1)**2*(5*i + 2)
Let y(h) = -2*h**4 + h**3 - 2*h**2. Let r = 21 - 15. Let p(i) = i**4 - i**3 + i**2. Let x(q) = r*y(q) + 10*p(q). Factor x(n).
-2*n**2*(n + 1)**2
Let l(k) = -16*k - 9*k**2 - 10 - 2 + 2 - k**3. Let q be l(-7). Factor 0 + 2/9*y**5 + 0*y - 2/9*y**3 + 0*y**q + 0*y**2.
2*y**3*(y - 1)*(y + 1)/9
Factor 0*w**2 - 8*w + 4*w - 6*w**2.
-2*w*(3*w + 2)
Let n(x) = 2*x**3 - 16*x**2 + 22*x - 10. Let w(v) = -v**3 + 16*v**2 - 23*v + 11. Let d(l) = 3*n(l) + 2*w(l). What is j in d(j) = 0?
1, 2
Suppose -8 - 4 = -3*f. Suppose 0*c - f = -c. Factor -2/7*l**3 + 0*l + 2/7*l**c - 2/7*l**2 + 0 + 2/7*l**5.
2*l**2*(l - 1)*(l + 1)**2/7
Let j(i) = -6*i. Let m be j(2). Let s be 8/6*(-3)/m. Solve 0 - 2/3*o + s*o**2 = 0.
0, 2
Suppose -5*s = 5*g - 20, 3*g = -s + 8 - 4. Find q such that 0*q - 2/7*q**3 + 2/7*q**4 + 0*q**2 + g = 0.
0, 1
Suppose l + 1 = -2*h, -3*h + 4*l - 23 = -5. Let z be 15/10 + h + 1. Factor 0*g + z*g**3 - 1/2*g**2 + 0.
g**2*(g - 1)/2
Let t(y) be the first derivative of -y**7/189 - y**6/45 - y**5/30 - y**4/54 - 8*y - 7. Let h(f) be the first derivative of t(f). Factor h(v).
-2*v**2*(v + 1)**3/9
Suppose q + 5 = 2*q. Let n be q/20 - (-11)/4. Determine l, given that -2*l + l - 4*l**3 + 2*l**2 + 3*l**n = 0.
0, 1
Let v(b) = b**3 - 5*b**2 - 5*b - 2. Let i be v(6). Suppose -5*t = -4*y + 7 + 10, y - t = i. Find o such that -o + 5*o**2 - y*o**2 - o**2 = 0.
0, 1
Let u = 26 - 20. Let l(c) be the second derivative of 0*c**2 - 3*c + 5/6*c**4 - 2/3*c**3 + 0 - 2/5*c**5 + 1/15*c**u. Factor l(o).
2*o*(o - 2)*(o - 1)**2
Let b be (-6)/(-12)*(2 + 0). Suppose -2 - b = -r. Suppose 2/5*p**2 - 2/5 + 2/5*p**r - 2/5*p = 0. What is p?
-1, 1
Let w(f) = -5*f**3 + f. Let j be w(-1). Suppose v - j = 0, 28 = 5*d - 2*v + 4*v. Factor 0 - r**3 + r**2 + 1/3*r**d - 1/3*r.
r*(r - 1)**3/3
Let t = 136/549 + 12/61. Factor t*p + 2/9*p**2 + 0.
2*p*(p + 2)/9
Let d(f) = -3*f**4 + 2*f**3 + 4*f**2 - 2*f - 3. Let t(o) = -o**4 + o**3 + o**2 - o - 1. Let z(q) = -5*d(q) + 10*t(q). Solve z(x) = 0.
-1, 1
Suppose 25 = -5*d - 0, -l = 5*d + 23. Factor 1/3*s**5 - 5/3*s + 2/3 - 4/3*s**4 + 4/3*s**3 + 2/3*s**l.
(s - 2)*(s - 1)**3*(s + 1)/3
Let z(h) = 3*h + 20. Let s be z(-6). Factor 0*o**4 + 3/4*o - o**3 - 1/2 + 1/2*o**s + 1/4*o**5.
(o - 1)**3*(o + 1)*(o + 2)/4
Determine h so that -2/9*h**3 + 1/9*h**4 + 0 + 8/9*h - 4/9*h**2 = 0.
-2, 0, 2
Suppose 3*i - 16 = g, -4*g - 118 = g + 4*i. Let v be 6/(-33) - 48/g. Factor 2/3*j**3 + 2*j + v*j**2 + 2/3.
2*(j + 1)**3/3
Factor 12/5*r**2 - 36/5 - 6/5*r**3 + 6*r.
-6*(r - 3)*(r - 1)*(r + 2)/5
Let m = 1466/1295 + 2/185. Factor 2/7*o**2 + 8/7 - m*o.
2*(o - 2)**2/7
Factor -3 - 4*j + 5 - 21*j**2 + 23*j**2.
2*(j - 1)**2
Suppose 11*f + 15 = 14*f. Suppose 5*v - 4*a - 1 = -11, f*a = -5*v + 35. Factor 24/5*z**v + 8/5*z + 0 + 18/5*z**3.
2*z*(3*z + 2)**2/5
Let t be (2 - -2)*4/16. Let s(c) be the first derivative of -2*c + 2/3*c**3 + t + 0*c**2. Solve s(r) = 0.
-1, 1
Suppose 142*q = 140*q + 52. Suppose 24*w + 6*w**4 + 16/3 + q*w**3 + 116/3*w**2 = 0. What is w?
-2, -1, -2/3
Factor 4*i - 1 + 9/4*i**3 - 21/4*i**2.
(i - 1)*(3*i - 2)**2/4
Let g(y) be the second derivative of 0*y**2 + 11/120*y**6 - 1/12*y**3 + 3/16*y**4 + 0 - 2*y - 1/56*y**7 - 3/16*y**5. Factor g(k).
-k*(k - 1)**3*(3*k - 2)/4
Suppose 0 = -4*t + 2*h + 18, h + 7 = 2. Factor 0 + 5/3*m**3 + 1/3*m**5 - 4/3*m**4 + 0*m - 2/3*m**t.
m**2*(m - 2)*(m - 1)**2/3
Find l, given that -5/2*l**4 + 5/2*l - 5/2*l**3 + 5/2*l**2 + 0 = 0.
-1, 0, 1
Let f(m) be the third derivative of 0 + m**2 + 1/168*m**8 - 1/10*m**5 + 1/18*m**4 + 0*m + 0*m**3 - 11/315*m**7 + 1/12*m**6. Find v, given that f(v) = 0.
0, 2/3, 1
Let o(s) be the third derivative of s**7/1785 + s**6/340 + s**5/255 + 8*s**2. Factor o(p).
2*p**2*(p + 1)*(p + 2)/17
Let w(x) be the first derivative of -400*x**3/3 + 120*x**2 - 36*x - 5. Factor w(a).
-4*(10*a - 3)**2
Factor 24/5*c**3 + 42/5*c**2 + 12/5*c - 6/5.
6*(c + 1)**2*(4*c - 1)/5
Let w(i) be the second derivative of 1/40*i**5 + 0 + 1/60*i**6 - 1/12*i**3 + 1/2*i**2 - 1/8*i**4 + 2*i. Factor w(l).
(l - 1)**2*(l + 1)*(l + 2)/2
Let c be (3 + (-29)/9)*(-18)/8. Let q(t) be the first derivative of -2 - 1/4*t**4 + t + c*t**2 - 1/3*t**3. Suppose q(k) = 0. Calculate k.
-1, 1
Let r = 617/5 + -123. Let 0*m - r*m**5 + 2/5*m**3 + 4/5*m**4 - 4/5*m**2 + 0 = 0. Calculate m.
-1, 0, 1, 2
Let y(h) be the first derivative of 2/5*h**5 - 2/15*h**6 + 3 + 0*h - 1/10*h**4 + 0*h**2 - 4/15*h**3. Find f such that y(f) = 0.
-1/2, 0, 1, 2
Suppose 0 = 4*v - 0*v. Suppose 2*d - 8 = f - 3, 0 = -5*d - 5*f + 5. Suppose -1/4*x**3 + 1/4*x + v + 0*x**d = 0. Calculate x.
-1, 0, 1
Suppose 13*q - 9*q = 12. Let g(d) = 6*d**4 + 2*d**3 + 6*d**2 + 10*d - 10. Let h(o) = 2*o**4 + o**3 + 2*o**2 + 3*o - 3. Let t(x) = q*g(x) - 10*h(x). Factor t(a).
-2*a**2*(a + 1)**2
Suppose -u = -2*u + 8. Suppose 0 = 5*q + u - 33. Factor 2*v**4 - 4*v**5 + q*v**5 - v**4.
v**4*(v + 1)
Let h(i) be the second derivative of i**4/84 + i**3/42 - i**2/7 + 61*i + 2. Factor h(k).
(k - 1)*(k + 2)/7
Let a(v) be the first derivative of -2 + 1/3*v**4 - 2/3*v + 11/9*v**3 + 5/6*v**2. Factor a(u).
(u + 1)*(u + 2)*(4*u - 1)/3
Let z = -380/9 - -4216/99. Factor 2/11*j**2 + z*j + 2/11.
2*(j + 1)**2/11
Let q(i) be the third derivative of -i**6/540 + i**3/2 - 2*i**2. Let x(t) be the first derivative of q(t). Determine d so that x(d) = 0.
0
Factor 2*x**4 + 4*x + 164*x**2 - 160*x**2 - 4*x**3 - 6*x**4.
-4*x*(x - 1)*(x + 1)**2
Let j(g) be the third derivative of 1/48*g**4 + 0*g + 1/240*g**5 + 0 + 0*g**3 + g**2. Factor j(i).
i*(i + 2)/4
Suppose 0 = -3*a - 0*a + 6. Suppose -4 = -a*c - 0. Find n such that c*n**5 - 4*n**2 + 4*n**4 + 2*n**4 - n + 4*n**3 - 5*n - 2 = 0.
-1, 1
Let r(p) = p + 6. Let j be r(-2). Let x(o) be the first derivative of 1/4*o**j - o - o**3 - 1 + 3/2*o**2. Factor x(v).
(v - 1)**3
Let v(h) = -h**3 + h**2 - 