x(x-10)=x-10

Solution for x(x-10)=x-10 equation:

Simplifying
x(x + -10) = x + -10

Reorder the terms:
x(-10 + x) = x + -10
(-10 * x + x * x) = x + -10
(-10x + x2) = x + -10

Reorder the terms:
-10x + x2 = -10 + x

Solving
-10x + x2 = -10 + x

Solving for variable 'x'.

Reorder the terms:
10 + -10x + -1x + x2 = -10 + x + 10 + -1x

Combine like terms: -10x + -1x = -11x
10 + -11x + x2 = -10 + x + 10 + -1x

Reorder the terms:
10 + -11x + x2 = -10 + 10 + x + -1x

Combine like terms: -10 + 10 = 0
10 + -11x + x2 = 0 + x + -1x
10 + -11x + x2 = x + -1x

Combine like terms: x + -1x = 0
10 + -11x + x2 = 0

Factor a trinomial.
(1 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {1, 10}