x(x-1)=x

Solution for x(x-1)=x equation:

Simplifying
x(x + -1) = x

Reorder the terms:
x(-1 + x) = x
(-1 * x + x * x) = x
(-1x + x2) = x

Solving
-1x + x2 = x

Solving for variable 'x'.

Reorder the terms:
-1x + -1x + x2 = x + -1x

Combine like terms: -1x + -1x = -2x
-2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-2x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + x) = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

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

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2
Solution
x = {0, 2}