(x^5)+x=0

Solution for (x^5)+x=0 equation:

Simplifying
(x5) + x = 0
x5 + x = 0

Reorder the terms:
x + x5 = 0

Solving
x + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x4) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x4)' equal to zero and attempt to solve:

Simplifying
1 + x4 = 0

Solving
1 + x4 = 0

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

Add '-1' to each side of the equation.
1 + -1 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x4 = 0 + -1
x4 = 0 + -1

Combine like terms: 0 + -1 = -1
x4 = -1

Simplifying
x4 = -1

The solution to this equation could not be determined.

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