(x-6)(x-6)=81

Solution for (x-6)(x-6)=81 equation:

Simplifying
(x + -6)(x + -6) = 81

Reorder the terms:
(-6 + x)(x + -6) = 81

Reorder the terms:
(-6 + x)(-6 + x) = 81

Multiply (-6 + x) * (-6 + x)
(-6(-6 + x) + x(-6 + x)) = 81
((-6 * -6 + x * -6) + x(-6 + x)) = 81
((36 + -6x) + x(-6 + x)) = 81
(36 + -6x + (-6 * x + x * x)) = 81
(36 + -6x + (-6x + x2)) = 81

Combine like terms: -6x + -6x = -12x
(36 + -12x + x2) = 81

Solving
36 + -12x + x2 = 81

Solving for variable 'x'.

Reorder the terms:
36 + -81 + -12x + x2 = 81 + -81

Combine like terms: 36 + -81 = -45
-45 + -12x + x2 = 81 + -81

Combine like terms: 81 + -81 = 0
-45 + -12x + x2 = 0

Factor a trinomial.
(-3 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(15 + -1x)' equal to zero and attempt to solve:

Simplifying
15 + -1x = 0

Solving
15 + -1x = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1x = 0 + -15
-1x = 0 + -15

Combine like terms: 0 + -15 = -15
-1x = -15

Divide each side by '-1'.
x = 15

Simplifying
x = 15
Solution
x = {-3, 15}