(b+6)(b+2)=-3

Solution for (b+6)(b+2)=-3 equation:

Simplifying
(b + 6)(b + 2) = -3

Reorder the terms:
(6 + b)(b + 2) = -3

Reorder the terms:
(6 + b)(2 + b) = -3

Multiply (6 + b) * (2 + b)
(6(2 + b) + b(2 + b)) = -3
((2 * 6 + b * 6) + b(2 + b)) = -3
((12 + 6b) + b(2 + b)) = -3
(12 + 6b + (2 * b + b * b)) = -3
(12 + 6b + (2b + b2)) = -3

Combine like terms: 6b + 2b = 8b
(12 + 8b + b2) = -3

Solving
12 + 8b + b2 = -3

Solving for variable 'b'.

Reorder the terms:
12 + 3 + 8b + b2 = -3 + 3

Combine like terms: 12 + 3 = 15
15 + 8b + b2 = -3 + 3

Combine like terms: -3 + 3 = 0
15 + 8b + b2 = 0

Factor a trinomial.
(5 + b)(3 + b) = 0

Subproblem 1
Set the factor '(5 + b)' equal to zero and attempt to solve:

Simplifying
5 + b = 0

Solving
5 + b = 0

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

Add '-5' to each side of the equation.
5 + -5 + b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + b = 0 + -5
b = 0 + -5

Combine like terms: 0 + -5 = -5
b = -5

Simplifying
b = -5
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 0

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

Add '-3' to each side of the equation.
3 + -3 + b = 0 + -3

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

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

Simplifying
b = -3
Solution
b = {-5, -3}