x^5+x^2=0

Solution for x^5+x^2=0 equation:

Simplifying
x5 + x2 = 0

Reorder the terms:
x2 + x5 = 0

Solving
x2 + x5 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(1 + x3) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + x3)' equal to zero and attempt to solve:

Simplifying
1 + x3 = 0

Solving
1 + x3 = 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 + x3 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x3 = 0 + -1
x3 = 0 + -1

Combine like terms: 0 + -1 = -1
x3 = -1

Simplifying
x3 = -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}