(x+2)(x+6)=5

Solution for (x+2)(x+6)=5 equation:

Simplifying
(x + 2)(x + 6) = 5

Reorder the terms:
(2 + x)(x + 6) = 5

Reorder the terms:
(2 + x)(6 + x) = 5

Multiply (2 + x) * (6 + x)
(2(6 + x) + x(6 + x)) = 5
((6 * 2 + x * 2) + x(6 + x)) = 5
((12 + 2x) + x(6 + x)) = 5
(12 + 2x + (6 * x + x * x)) = 5
(12 + 2x + (6x + x2)) = 5

Combine like terms: 2x + 6x = 8x
(12 + 8x + x2) = 5

Solving
12 + 8x + x2 = 5

Solving for variable 'x'.

Reorder the terms:
12 + -5 + 8x + x2 = 5 + -5

Combine like terms: 12 + -5 = 7
7 + 8x + x2 = 5 + -5

Combine like terms: 5 + -5 = 0
7 + 8x + x2 = 0

Factor a trinomial.
(7 + x)(1 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-7, -1}