(x+6)(x+6)-1=8

Solution for (x+6)(x+6)-1=8 equation:

Simplifying
(x + 6)(x + 6) + -1 = 8

Reorder the terms:
(6 + x)(x + 6) + -1 = 8

Reorder the terms:
(6 + x)(6 + x) + -1 = 8

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) + -1 = 8
((6 * 6 + x * 6) + x(6 + x)) + -1 = 8
((36 + 6x) + x(6 + x)) + -1 = 8
(36 + 6x + (6 * x + x * x)) + -1 = 8
(36 + 6x + (6x + x2)) + -1 = 8

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) + -1 = 8

Reorder the terms:
36 + -1 + 12x + x2 = 8

Combine like terms: 36 + -1 = 35
35 + 12x + x2 = 8

Solving
35 + 12x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
35 + -8 + 12x + x2 = 8 + -8

Combine like terms: 35 + -8 = 27
27 + 12x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
27 + 12x + x2 = 0

Factor a trinomial.
(9 + x)(3 + x) = 0

Subproblem 1
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 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 + x = 0 + -9

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

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

Simplifying
x = -9
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {-9, -3}