2t^5-32t=0

Solution for 2t^5-32t=0 equation:

Simplifying
2t5 + -32t = 0

Reorder the terms:
-32t + 2t5 = 0

Solving
-32t + 2t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2t'.
2t(-16 + t4) = 0

Factor a difference between two squares.
2t((4 + t2)(-4 + t2)) = 0

Factor a difference between two squares.
2t((4 + t2)((2 + t)(-2 + t))) = 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.
Subproblem 3
Set the factor '(2 + t)' equal to zero and attempt to solve:

Simplifying
2 + t = 0

Solving
2 + t = 0

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

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

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

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

Simplifying
t = -2
Subproblem 4
Set the factor '(-2 + t)' equal to zero and attempt to solve:

Simplifying
-2 + t = 0

Solving
-2 + t = 0

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

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

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

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

Simplifying
t = 2
Solution
t = {0, -2, 2}