g^5-g=

Solution for g^5-g= equation:

Simplifying
g5 + -1g = 0

Reorder the terms:
-1g + g5 = 0

Solving
-1g + g5 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), 'g'.
g(-1 + g4) = 0

Factor a difference between two squares.
g((1 + g2)(-1 + g2)) = 0

Factor a difference between two squares.
g((1 + g2)((1 + g)(-1 + g))) = 0

Subproblem 1
Set the factor 'g' equal to zero and attempt to solve:

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0
Subproblem 2
Set the factor '(1 + g2)' equal to zero and attempt to solve:

Simplifying
1 + g2 = 0

Solving
1 + g2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + g2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + g2 = 0 + -1
g2 = 0 + -1

Combine like terms: 0 + -1 = -1
g2 = -1

Simplifying
g2 = -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 + g)' equal to zero and attempt to solve:

Simplifying
1 + g = 0

Solving
1 + g = 0

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

Add '-1' to each side of the equation.
1 + -1 + g = 0 + -1

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

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

Simplifying
g = -1
Subproblem 4
Set the factor '(-1 + g)' equal to zero and attempt to solve:

Simplifying
-1 + g = 0

Solving
-1 + g = 0

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

Add '1' to each side of the equation.
-1 + 1 + g = 0 + 1

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

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

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