(x-13)(x-4)=x-13

Solution for (x-13)(x-4)=x-13 equation:

Simplifying
(x + -13)(x + -4) = x + -13

Reorder the terms:
(-13 + x)(x + -4) = x + -13

Reorder the terms:
(-13 + x)(-4 + x) = x + -13

Multiply (-13 + x) * (-4 + x)
(-13(-4 + x) + x(-4 + x)) = x + -13
((-4 * -13 + x * -13) + x(-4 + x)) = x + -13
((52 + -13x) + x(-4 + x)) = x + -13
(52 + -13x + (-4 * x + x * x)) = x + -13
(52 + -13x + (-4x + x2)) = x + -13

Combine like terms: -13x + -4x = -17x
(52 + -17x + x2) = x + -13

Reorder the terms:
52 + -17x + x2 = -13 + x

Solving
52 + -17x + x2 = -13 + x

Solving for variable 'x'.

Reorder the terms:
52 + 13 + -17x + -1x + x2 = -13 + x + 13 + -1x

Combine like terms: 52 + 13 = 65
65 + -17x + -1x + x2 = -13 + x + 13 + -1x

Combine like terms: -17x + -1x = -18x
65 + -18x + x2 = -13 + x + 13 + -1x

Reorder the terms:
65 + -18x + x2 = -13 + 13 + x + -1x

Combine like terms: -13 + 13 = 0
65 + -18x + x2 = 0 + x + -1x
65 + -18x + x2 = x + -1x

Combine like terms: x + -1x = 0
65 + -18x + x2 = 0

Factor a trinomial.
(5 + -1x)(13 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {5, 13}