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

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

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

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

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

Multiply (5 + x) * (6 + x)
(5(6 + x) + x(6 + x)) = 2
((6 * 5 + x * 5) + x(6 + x)) = 2
((30 + 5x) + x(6 + x)) = 2
(30 + 5x + (6 * x + x * x)) = 2
(30 + 5x + (6x + x2)) = 2

Combine like terms: 5x + 6x = 11x
(30 + 11x + x2) = 2

Solving
30 + 11x + x2 = 2

Solving for variable 'x'.

Reorder the terms:
30 + -2 + 11x + x2 = 2 + -2

Combine like terms: 30 + -2 = 28
28 + 11x + x2 = 2 + -2

Combine like terms: 2 + -2 = 0
28 + 11x + x2 = 0

Factor a trinomial.
(7 + x)(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {-7, -4}