n^5+n=0

Solution for n^5+n=0 equation:

Simplifying
n5 + n = 0

Reorder the terms:
n + n5 = 0

Solving
n + n5 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(1 + n4) = 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 + n4)' equal to zero and attempt to solve:

Simplifying
1 + n4 = 0

Solving
1 + n4 = 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 + n4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n4 = 0 + -1
n4 = 0 + -1

Combine like terms: 0 + -1 = -1
n4 = -1

Simplifying
n4 = -1

The solution to this equation could not be determined.

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