(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.
(-15 + -1x)(3 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-15, 3}