2t^3(t^2+t-64)=0

Solution for 2t^3(t^2+t-64)=0 equation:

Simplifying
2t3(t2 + t + -64) = 0

Reorder the terms:
2t3(-64 + t + t2) = 0
(-64 * 2t3 + t * 2t3 + t2 * 2t3) = 0
(-128t3 + 2t4 + 2t5) = 0

Solving
-128t3 + 2t4 + 2t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t3'.
2t3(-64 + t + t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 't3' equal to zero and attempt to solve:

Simplifying
t3 = 0

Solving
t3 = 0

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

Simplifying
t3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-64 + t + t2)' equal to zero and attempt to solve:

Simplifying
-64 + t + t2 = 0

Solving
-64 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + t + 64 + t2 = 0 + 64

Reorder the terms:
-64 + 64 + t + t2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + t + t2 = 0 + 64
t + t2 = 0 + 64

Combine like terms: 0 + 64 = 64
t + t2 = 64

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 64 + 0.25

Reorder the terms:
0.25 + t + t2 = 64 + 0.25

Combine like terms: 64 + 0.25 = 64.25
0.25 + t + t2 = 64.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 64.25

Calculate the square root of the right side: 8.015609771

Break this problem into two subproblems by setting 
(t + 0.5) equal to 8.015609771 and -8.015609771.

Subproblem 1
t + 0.5 = 8.015609771

Simplifying
t + 0.5 = 8.015609771

Reorder the terms:
0.5 + t = 8.015609771

Solving
0.5 + t = 8.015609771

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 8.015609771 + -0.5
t = 8.015609771 + -0.5

Combine like terms: 8.015609771 + -0.5 = 7.515609771
t = 7.515609771

Simplifying
t = 7.515609771

Subproblem 2
t + 0.5 = -8.015609771

Simplifying
t + 0.5 = -8.015609771

Reorder the terms:
0.5 + t = -8.015609771

Solving
0.5 + t = -8.015609771

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -8.015609771 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -8.015609771 + -0.5
t = -8.015609771 + -0.5

Combine like terms: -8.015609771 + -0.5 = -8.515609771
t = -8.515609771

Simplifying
t = -8.515609771

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.515609771, -8.515609771}
Solution
t = {7.515609771, -8.515609771}