x(x-3)=x-3

Solution for x(x-3)=x-3 equation:

Simplifying
x(x + -3) = x + -3

Reorder the terms:
x(-3 + x) = x + -3
(-3 * x + x * x) = x + -3
(-3x + x2) = x + -3

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

Solving
-3x + x2 = -3 + x

Solving for variable 'x'.

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

Combine like terms: -3x + -1x = -4x
3 + -4x + x2 = -3 + x + 3 + -1x

Reorder the terms:
3 + -4x + x2 = -3 + 3 + x + -1x

Combine like terms: -3 + 3 = 0
3 + -4x + x2 = 0 + x + -1x
3 + -4x + x2 = x + -1x

Combine like terms: x + -1x = 0
3 + -4x + x2 = 0

Factor a trinomial.
(1 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1, 3}