 450*t = 0. Calculate t.
-1, 0, 2, 5, 75
Factor 2*p**2 - 773*p/2 + 193/2.
(p - 193)*(4*p - 1)/2
Let -5*z**2 - 540*z - 1575 = 0. Calculate z.
-105, -3
Determine u so that -u**2 + 3*u - 2 = 0.
1, 2
Let 22*b**4/7 + 4*b**3/7 - 88*b**2/7 - 16*b/7 = 0. What is b?
-2, -2/11, 0, 2
Factor -2*b**4 - 4*b**3 + 2*b**2 + 4*b.
-2*b*(b - 1)*(b + 1)*(b + 2)
Find z such that 2*z**3/11 - 38*z**2/11 + 140*z/11 = 0.
0, 5, 14
Find x, given that -2*x**4/7 + 160*x**3/7 + 494*x**2/7 + 332*x/7 = 0.
-2, -1, 0, 83
Factor 4*b**3/5 + 22*b**2/5 + 34*b/5 + 12/5.
2*(b + 2)*(b + 3)*(2*b + 1)/5
Find c such that 2*c**5/7 + 22*c**4/7 - 4*c**3/7 - 44*c**2/7 + 2*c/7 + 22/7 = 0.
-11, -1, 1
Find q such that q**4 + 12*q**3 + 42*q**2 + 52*q + 21 = 0.
-7, -3, -1
Factor 7*q**3/4 + 605*q**2 + 1723*q/4 - 345/2.
(q + 1)*(q + 345)*(7*q - 2)/4
Determine a so that -2*a**2/11 + 2*a/11 = 0.
0, 1
Suppose 128*p**5/3 - 320*p**4/3 + 104*p**3/3 + 40*p**2 + 6*p = 0. What is p?
-1/4, 0, 3/2
Let -z**4 - 33*z**3 - 62*z**2 = 0. What is z?
-31, -2, 0
Factor -4*r**2 + 220*r - 624.
-4*(r - 52)*(r - 3)
Determine w so that 5*w**2 - 375*w - 380 = 0.
-1, 76
Solve 3*v**2/5 - 381*v/5 + 2178/5 = 0.
6, 121
Suppose -16*q**5/3 + 196*q**4/3 - 176*q**3 + 568*q**2/3 - 256*q/3 + 12 = 0. Calculate q.
1/4, 1, 9
Let 6*f**4/7 + 18*f**3/7 - 144*f**2/7 - 480*f/7 = 0. What is f?
-4, 0, 5
Factor 5*o**2 + 50*o + 80.
5*(o + 2)*(o + 8)
Let -170*r**4 + 505*r**3 + 15*r**2 = 0. What is r?
-1/34, 0, 3
Let 120*t**5 - 33*t**4 - 366*t**3 - 141*t**2 + 84*t + 12 = 0. Calculate t.
-1, -1/8, 2/5, 2
Factor -2*t**2/7 + 128*t/7 - 1950/7.
-2*(t - 39)*(t - 25)/7
Factor -b**4 - 43*b**3 - 156*b**2.
-b**2*(b + 4)*(b + 39)
Let 400*z**4/9 + 7040*z**3/9 + 10516*z**2/9 + 1484*z/3 + 64 = 0. Calculate z.
-16, -1, -3/10
Let -5*h**2 + 40*h - 75 = 0. Calculate h.
3, 5
Factor -3*f**4/2 + 9*f**3/2 + 6*f**2.
-3*f**2*(f - 4)*(f + 1)/2
Find o, given that -2*o**5/7 - 2*o**4 + 4*o**3/7 + 4*o**2 - 2*o/7 - 2 = 0.
-7, -1, 1
Suppose -4*k**4/5 - 12*k**3/5 + 8*k**2/5 + 48*k/5 + 32/5 = 0. Calculate k.
-2, -1, 2
Factor 2*b**4/7 + 12*b**3/7 + 8*b**2/7 - 12*b/7 - 10/7.
2*(b - 1)*(b + 1)**2*(b + 5)/7
Find z, given that 2*z**4 + 100*z**3 + 90*z**2 - 400*z - 392 = 0.
-49, -2, -1, 2
Factor -9*u**2 - 66*u - 21.
-3*(u + 7)*(3*u + 1)
Factor -3*l**4/2 + 9*l**3 - 3*l**2/2 - 36*l - 24.
-3*(l - 4)**2*(l + 1)**2/2
Factor -j**5 - 6*j**4 + j**3 + 6*j**2.
-j**2*(j - 1)*(j + 1)*(j + 6)
Suppose -3*f**4/8 - 4035*f**3/2 - 16281225*f**2/4 - 7299415875*f/2 - 9817714351875/8 = 0. What is f?
-1345
Factor 3*y**4/7 + 33*y**3/7 - 171*y**2/7 + 135*y/7.
3*y*(y - 3)*(y - 1)*(y + 15)/7
Suppose -k**4 + 7*k**3 - k**2 - 27*k - 18 = 0. What is k?
-1, 3, 6
Determine o so that -2*o**4 + 24*o**3 + 88*o**2 - 960*o - 3200 = 0.
-4, 10
Suppose 3*d**5/5 - 12*d**4/5 - 213*d**3/5 + 1206*d**2/5 - 108*d - 1944/5 = 0. Calculate d.
-9, -1, 2, 6
Factor -2*m**3/11 + 86*m**2/11 - 966*m/11 + 882/11.
-2*(m - 21)**2*(m - 1)/11
Find h, given that 196*h**4 - 9296*h**3 + 107536*h**2 + 63744*h + 9216 = 0.
-2/7, 24
Suppose 2*n**4 + 46*n**3 - 324*n**2 + 680*n - 464 = 0. Calculate n.
-29, 2
Factor -3*k**4/2 + 21*k**3/2.
-3*k**3*(k - 7)/2
Factor -h**4/8 - 39*h**3/8 + 53*h**2/2 - 87*h/2 + 22.
-(h - 2)**2*(h - 1)*(h + 44)/8
Let -5*c**5 - 50*c**4 - 75*c**3 + 50*c**2 + 80*c = 0. Calculate c.
-8, -2, -1, 0, 1
Factor 11*s**2/8 + 115*s/2.
s*(11*s + 460)/8
Factor 2*p**2 - 4382*p - 4384.
2*(p - 2192)*(p + 1)
Factor -h**2/6 + 331*h/6 + 166/3.
-(h - 332)*(h + 1)/6
Determine h, given that h**3 - 37*h**2 - 77*h - 39 = 0.
-1, 39
Factor 4*a**2/11 + 7*a/11 - 2/11.
(a + 2)*(4*a - 1)/11
Factor 3*k**3/5 + 42*k**2/5 - 3*k/5 - 42/5.
3*(k - 1)*(k + 1)*(k + 14)/5
Suppose -8*w**5 + 12*w**4 + 160*w**3 - 84*w**2 - 80*w = 0. What is w?
-4, -1/2, 0, 1, 5
Suppose -4*r**3 - 8*r**2 + 252*r = 0. Calculate r.
-9, 0, 7
Factor 2*j**2/13 - 18*j.
2*j*(j - 117)/13
Factor 3*c**2 - 4194*c + 1465803.
3*(c - 699)**2
Factor 2*w**5/7 - 4*w**4/7 + 4*w**2/7 - 2*w/7.
2*w*(w - 1)**3*(w + 1)/7
Determine w, given that w**3/4 + 11*w**2 + 85*w/4 + 21/2 = 0.
-42, -1
Find m, given that -3*m**5 + 6*m**4 + 3*m**3 - 6*m**2 = 0.
-1, 0, 1, 2
Let c**3 - 18*c**2 + 69*c/4 - 17/4 = 0. What is c?
1/2, 17
Let -o**4 + 210*o**3 - 10153*o**2 - 91560*o - 190096 = 0. What is o?
-4, 109
Find g such that -8*g**4 - 122*g**3 - 462*g**2 - 428*g - 80 = 0.
-10, -4, -1, -1/4
Factor 2*d**3/7 + 76*d**2/7 - 242*d/7 + 164/7.
2*(d - 2)*(d - 1)*(d + 41)/7
Find z, given that 3*z**3/8 + z**2/4 - 3*z/8 - 1/4 = 0.
-1, -2/3, 1
Factor -y**3/2 - 5*y**2/2 + 3*y.
-y*(y - 1)*(y + 6)/2
Determine x, given that -144*x**5 + 1020*x**4 - 76*x**3 - 57*x**2 + 7*x = 0.
-1/4, 0, 1/6, 7
Factor 2*v**2/9 + 70*v/9 + 68/9.
2*(v + 1)*(v + 34)/9
Factor v**5 + 6*v**4 + 12*v**3 + 10*v**2 + 3*v.
v*(v + 1)**3*(v + 3)
Factor 3*b**2/7 - 267*b/7 - 78.
3*(b - 91)*(b + 2)/7
Solve -4*g**4/9 - 604*g**3/9 - 22496*g**2/9 + 23104*g/9 = 0 for g.
-76, 0, 1
Factor 4*i**2 + 2048*i + 262144.
4*(i + 256)**2
What is n in -2*n**5 + 22*n**3 - 36*n**2 + 16*n = 0?
-4, 0, 1, 2
Let -f**4 - 2*f**3 + 4*f**2 + 8*f = 0. Calculate f.
-2, 0, 2
Factor -g**4/4 + 3*g**3 + 7*g**2.
-g**2*(g - 14)*(g + 2)/4
Suppose -7*u**4/3 + 23*u**3/3 - 9*u**2 + 13*u/3 - 2/3 = 0. What is u?
2/7, 1
Let -52*n**2 - 668*n + 104 = 0. What is n?
-13, 2/13
Let -529*z**2 + 22724*z - 244036 = 0. What is z?
494/23
Factor 4*d**3 - 1336*d**2/7 + 3396*d/7 + 1080/7.
4*(d - 45)*(d - 3)*(7*d + 2)/7
Let -21*q**4 + 37548*q**3 - 117487680*q**2/7 - 21456*q/7 + 9590832/7 = 0. What is q?
-2/7, 2/7, 894
Factor 9*x**5/5 + 21*x**4/5 - 24*x**3/5 - 12*x**2.
3*x**2*(x + 2)**2*(3*x - 5)/5
Determine m, given that -54*m**3/7 + 90*m**2 - 402*m/7 + 66/7 = 0.
1/3, 11
What is m in -5*m**4 - 220*m**3 - 2630*m**2 - 4620*m - 2205 = 0?
-21, -1
Find n, given that 2*n**5 - 136*n**4 - 864*n**3 - 1756*n**2 - 1474*n - 444 = 0.
-3, -1, 74
Determine u, given that -55*u**3 - 5125*u**2 - 930*u = 0.
-93, -2/11, 0
Factor -g**5 + 18*g**4 - 60*g**3 - 200*g**2.
-g**2*(g - 10)**2*(g + 2)
Suppose -5*q**3 - 12345*q**2 - 10159935*q - 2787208835 = 0. Calculate q.
-823
Determine z so that 9*z**4 - 21*z**3 + 12*z = 0.
-2/3, 0, 1, 2
Find f, given that f**4 + 52*f**3 + 47*f**2 - 208*f - 204 = 0.
-51, -2, -1, 2
Factor 2*h**3 + 8*h**2/3 - 10*h/3 - 4/3.
2*(h - 1)*(h + 2)*(3*h + 1)/3
Solve z**5/5 - 11*z**4 - 293*z**3/5 - 417*z**2/5 - 36*z = 0 for z.
-3, -1, 0, 60
Factor 2*u**2/9 - 10*u/9 + 8/9.
2*(u - 4)*(u - 1)/9
Factor z**4/2 + 3*z**3 - 2*z**2 - 12*z.
z*(z - 2)*(z + 2)*(z + 6)/2
Factor 2*h**2/7 - 6262*h/7.
2*h*(h - 3131)/7
Determine o, given that -3*o**4/2 - 3*o**3 + 3*o**2/2 + 3*o = 0.
-2, -1, 0, 1
Factor -2*z**2 - 4300*z - 4298.
-2*(z + 1)*(z + 2149)
Factor 2*v**3/9 + 4*v**2/3 + 2*v/3 - 20/9.
2*(v - 1)*(v + 2)*(v + 5)/9
Factor -d**2/6 - 7*d/3 - 11/2.
-(d + 3)*(d + 11)/6
Determine v, given that -5*v**5/6 + 5*v**4 + 35*v**3/3 - 30*v**2 - 425*v/6 - 35 = 0.
-2, -1, 3, 7
Factor p**5/5 - p**4/5 - 4*p**3/5 + 4*p**2/5.
p**2*(p - 2)*(p - 1)*(p + 2)/5
Factor 2*h**2/11 - 492*h/11.
2*h*(h - 246)/11
Find p such that -2*p**2/5 - 588*p/5 = 0.
-294, 0
Factor x**2/5 + 24*x/5 + 44/5.
(x + 2)*(x + 22)/5
What is w in 3*w**2/4 + 33*w/4 - 39/2 = 0?
-13, 2
Suppose -d**3/2 - 3*d**2 - 9*d/2 = 0. Calculate d.
-3, 0
Suppose -3*q**2/5 + 294*q/5 + 297/5 = 0. Calculate q.
-1, 99
Factor -3*s**3/4 - 6*s**2 + 69*s/4 + 45/2.
-3*(s - 3)*(s + 1)*(s + 10)/4
Let -2*o**3/13 + 1172*o**2/13 + 2350*o/13 + 1176/13 = 0. Calculate o.
-1, 588
Determine h, given that -30*h**2/7 - 4*h = 0.
-14/15, 0
Let -d**2 - 18*d - 65 = 0. Calculate d.
-13, -5
Factor 3*v**3 + 72*v**2 + 351*v - 1014.
3*(v - 2)*(v + 13)**2
Let -w**2 - 8*w - 12 = 0. What is w?
-6, -2
Factor -h**3/8 - 31*h**2/8 - 25*h/4 + 29.
-(h - 2)*(h + 4)*(h + 29)/8
Suppose -3*n**5/2 + 132*n**3 + 531*n**2 + 459*n/2 - 891 = 0. What is n?
-6, -3, 1, 11
Factor 4*c**4 + 112*c**3 + 108*c**2.
4*c**2*(c + 1)*(c + 27)
Factor -9*y**3 - 15*y**2 - 6*y.
-3*y*(y + 1)*(3*y + 2)
Suppose -5*l**2 - 150*l - 520 = 0. Calculate l.
-26, -4
Find m, given that -m**2/4 + 40*m - 1600 = 0.
80
Factor -2*s**2/17 - 48*s/17 - 288/17.
-2*(s + 12)**2/17
Solve -2*x**2 - 34*x + 36 = 0 for x.
-18, 1
What is a in -4*a**2/3 + 896*a/9 - 592/9 = 0?
2/3, 74
Determine u so that u**3 - 10*u**2 - 100*u + 1000 = 0.
-10, 10
Factor -t**3 - 90*t**2 - 825*t - 2000.
-(t + 5)**2*(t + 80)
Let -5*q**