x(x-8)=x-20

Solution for x(x-8)=x-20 equation:

Simplifying
x(x + -8) = x + -20

Reorder the terms:
x(-8 + x) = x + -20
(-8 * x + x * x) = x + -20
(-8x + x2) = x + -20

Reorder the terms:
-8x + x2 = -20 + x

Solving
-8x + x2 = -20 + x

Solving for variable 'x'.

Reorder the terms:
20 + -8x + -1x + x2 = -20 + x + 20 + -1x

Combine like terms: -8x + -1x = -9x
20 + -9x + x2 = -20 + x + 20 + -1x

Reorder the terms:
20 + -9x + x2 = -20 + 20 + x + -1x

Combine like terms: -20 + 20 = 0
20 + -9x + x2 = 0 + x + -1x
20 + -9x + x2 = x + -1x

Combine like terms: x + -1x = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {4, 5}