2t^3+8t=0

Solution for 2t^3+8t=0 equation:

Simplifying
2t3 + 8t = 0

Reorder the terms:
8t + 2t3 = 0

Solving
8t + 2t3 = 0

Solving for variable 't'.

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

Ignore the factor 2.
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 '(4 + t2)' equal to zero and attempt to solve:

Simplifying
4 + t2 = 0

Solving
4 + t2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + t2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + t2 = 0 + -4
t2 = 0 + -4

Combine like terms: 0 + -4 = -4
t2 = -4

Simplifying
t2 = -4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}