x(x^5-1)=0

Solution for x(x^5-1)=0 equation:

Simplifying
x(x5 + -1) = 0

Reorder the terms:
x(-1 + x5) = 0
(-1 * x + x5 * x) = 0
(-1x + x6) = 0

Solving
-1x + x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + 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 '(-1 + x5)' equal to zero and attempt to solve:

Simplifying
-1 + x5 = 0

Solving
-1 + x5 = 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 + x5 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x5 = 0 + 1
x5 = 0 + 1

Combine like terms: 0 + 1 = 1
x5 = 1

Simplifying
x5 = 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}