(x+6)(x+6)-4(x+6)=0

Solution for (x+6)(x+6)-4(x+6)=0 equation:

Simplifying
(x + 6)(x + 6) + -4(x + 6) = 0

Reorder the terms:
(6 + x)(x + 6) + -4(x + 6) = 0

Reorder the terms:
(6 + x)(6 + x) + -4(x + 6) = 0

Multiply (6 + x) * (6 + x)
(6(6 + x) + x(6 + x)) + -4(x + 6) = 0
((6 * 6 + x * 6) + x(6 + x)) + -4(x + 6) = 0
((36 + 6x) + x(6 + x)) + -4(x + 6) = 0
(36 + 6x + (6 * x + x * x)) + -4(x + 6) = 0
(36 + 6x + (6x + x2)) + -4(x + 6) = 0

Combine like terms: 6x + 6x = 12x
(36 + 12x + x2) + -4(x + 6) = 0

Reorder the terms:
36 + 12x + x2 + -4(6 + x) = 0
36 + 12x + x2 + (6 * -4 + x * -4) = 0
36 + 12x + x2 + (-24 + -4x) = 0

Reorder the terms:
36 + -24 + 12x + -4x + x2 = 0

Combine like terms: 36 + -24 = 12
12 + 12x + -4x + x2 = 0

Combine like terms: 12x + -4x = 8x
12 + 8x + x2 = 0

Solving
12 + 8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(2 + x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-6, -2}