t^5-t=

Solution for t^5-t= equation:

Simplifying
t5 + -1t = 0

Reorder the terms:
-1t + t5 = 0

Solving
-1t + t5 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(-1 + t4) = 0

Factor a difference between two squares.
t((1 + t2)(-1 + t2)) = 0

Factor a difference between two squares.
t((1 + t2)((1 + t)(-1 + t))) = 0

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 '(1 + t2)' equal to zero and attempt to solve:

Simplifying
1 + t2 = 0

Solving
1 + t2 = 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 + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + t2 = 0 + -1
t2 = 0 + -1

Combine like terms: 0 + -1 = -1
t2 = -1

Simplifying
t2 = -1

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 '(1 + t)' equal to zero and attempt to solve:

Simplifying
1 + t = 0

Solving
1 + t = 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 + t = 0 + -1

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

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

Simplifying
t = -1
Subproblem 4
Set the factor '(-1 + t)' equal to zero and attempt to solve:

Simplifying
-1 + t = 0

Solving
-1 + t = 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 + t = 0 + 1

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

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

Simplifying
t = 1
Solution
t = {0, -1, 1}