x^4=x

Solution for x^4=x equation:

Simplifying
x4 = x

Solving
x4 = x

Solving for variable 'x'.

Reorder the terms:
-1x + x4 = x + -1x

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x3) = 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 + 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}