(x-6)(x-6)=x

Solution for (x-6)(x-6)=x equation:

Simplifying
(x + -6)(x + -6) = x

Reorder the terms:
(-6 + x)(x + -6) = x

Reorder the terms:
(-6 + x)(-6 + x) = x

Multiply (-6 + x) * (-6 + x)
(-6(-6 + x) + x(-6 + x)) = x
((-6 * -6 + x * -6) + x(-6 + x)) = x
((36 + -6x) + x(-6 + x)) = x
(36 + -6x + (-6 * x + x * x)) = x
(36 + -6x + (-6x + x2)) = x

Combine like terms: -6x + -6x = -12x
(36 + -12x + x2) = x

Solving
36 + -12x + x2 = x

Solving for variable 'x'.

Reorder the terms:
36 + -12x + -1x + x2 = x + -1x

Combine like terms: -12x + -1x = -13x
36 + -13x + x2 = x + -1x

Combine like terms: x + -1x = 0
36 + -13x + x2 = 0

Factor a trinomial.
(4 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

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

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

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {4, 9}