x^6+32x=0

Solution for x^6+32x=0 equation:

Simplifying
x6 + 32x = 0

Reorder the terms:
32x + x6 = 0

Solving
32x + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(32 + x5) = 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 '(32 + x5)' equal to zero and attempt to solve:

Simplifying
32 + x5 = 0

Solving
32 + x5 = 0

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

Add '-32' to each side of the equation.
32 + -32 + x5 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + x5 = 0 + -32
x5 = 0 + -32

Combine like terms: 0 + -32 = -32
x5 = -32

Simplifying
x5 = -32

The solution to this equation could not be determined.

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