(x-8)(x-5)=x

Solution for (x-8)(x-5)=x equation:

Simplifying
(x + -8)(x + -5) = x

Reorder the terms:
(-8 + x)(x + -5) = x

Reorder the terms:
(-8 + x)(-5 + x) = x

Multiply (-8 + x) * (-5 + x)
(-8(-5 + x) + x(-5 + x)) = x
((-5 * -8 + x * -8) + x(-5 + x)) = x
((40 + -8x) + x(-5 + x)) = x
(40 + -8x + (-5 * x + x * x)) = x
(40 + -8x + (-5x + x2)) = x

Combine like terms: -8x + -5x = -13x
(40 + -13x + x2) = x

Solving
40 + -13x + x2 = x

Solving for variable 'x'.

Reorder the terms:
40 + -13x + -1x + x2 = x + -1x

Combine like terms: -13x + -1x = -14x
40 + -14x + x2 = x + -1x

Combine like terms: x + -1x = 0
40 + -14x + x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -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 '(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 = {4, 10}