64t^2+32t^3=-24t

Solution for 64t^2+32t^3=-24t equation:

Simplifying
64t2 + 32t3 = -24t

Solving
64t2 + 32t3 = -24t

Solving for variable 't'.

Reorder the terms:
24t + 64t2 + 32t3 = -24t + 24t

Combine like terms: -24t + 24t = 0
24t + 64t2 + 32t3 = 0

Factor out the Greatest Common Factor (GCF), '8t'.
8t(3 + 8t + 4t2) = 0

Factor a trinomial.
8t((3 + 2t)(1 + 2t)) = 0

Ignore the factor 8.
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 '(3 + 2t)' equal to zero and attempt to solve:

Simplifying
3 + 2t = 0

Solving
3 + 2t = 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 + 2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2t = 0 + -3
2t = 0 + -3

Combine like terms: 0 + -3 = -3
2t = -3

Divide each side by '2'.
t = -1.5

Simplifying
t = -1.5
Subproblem 3
Set the factor '(1 + 2t)' equal to zero and attempt to solve:

Simplifying
1 + 2t = 0

Solving
1 + 2t = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2t = 0 + -1
2t = 0 + -1

Combine like terms: 0 + -1 = -1
2t = -1

Divide each side by '2'.
t = -0.5

Simplifying
t = -0.5
Solution
t = {0, -1.5, -0.5}