8t^2-4t^3=-60t

Solution for 8t^2-4t^3=-60t equation:

Simplifying
8t2 + -4t3 = -60t

Solving
8t2 + -4t3 = -60t

Solving for variable 't'.

Reorder the terms:
60t + 8t2 + -4t3 = -60t + 60t

Combine like terms: -60t + 60t = 0
60t + 8t2 + -4t3 = 0

Factor out the Greatest Common Factor (GCF), '4t'.
4t(15 + 2t + -1t2) = 0

Factor a trinomial.
4t((5 + -1t)(3 + t)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

Move all terms containing t to the left, all other terms to the right.

Simplifying
t = 0
Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Subproblem 3
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + t = 0 + -3
t = 0 + -3

Combine like terms: 0 + -3 = -3
t = -3

Simplifying
t = -3
Solution
t = {0, 5, -3}