n-n^5=0

Solution for n-n^5=0 equation:

Simplifying
n + -1n5 = 0

Solving
n + -1n5 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + -1n4) = 0

Factor a difference between two squares.
n((1 + n2)(1 + -1n2)) = 0

Factor a difference between two squares.
n((1 + n2)((1 + n)(1 + -1n))) = 0

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

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(1 + n2)' equal to zero and attempt to solve:

Simplifying
1 + n2 = 0

Solving
1 + n2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + n2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n2 = 0 + -1
n2 = 0 + -1

Combine like terms: 0 + -1 = -1
n2 = -1

Simplifying
n2 = -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 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

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

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

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

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

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

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

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

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

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

Divide each side by '-1'.
n = 1

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