x(x-2)=(x-2)

Solution for x(x-2)=(x-2) equation:

Simplifying
x(x + -2) = (x + -2)

Reorder the terms:
x(-2 + x) = (x + -2)
(-2 * x + x * x) = (x + -2)
(-2x + x2) = (x + -2)

Reorder the terms:
-2x + x2 = (-2 + x)

Remove parenthesis around (-2 + x)
-2x + x2 = -2 + x

Solving
-2x + x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
2 + -2x + -1x + x2 = -2 + x + 2 + -1x

Combine like terms: -2x + -1x = -3x
2 + -3x + x2 = -2 + x + 2 + -1x

Reorder the terms:
2 + -3x + x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
2 + -3x + x2 = 0 + x + -1x
2 + -3x + x2 = x + -1x

Combine like terms: x + -1x = 0
2 + -3x + x2 = 0

Factor a trinomial.
(1 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}