(b+8)(b+4)=5

Solution for (b+8)(b+4)=5 equation:

Simplifying
(b + 8)(b + 4) = 5

Reorder the terms:
(8 + b)(b + 4) = 5

Reorder the terms:
(8 + b)(4 + b) = 5

Multiply (8 + b) * (4 + b)
(8(4 + b) + b(4 + b)) = 5
((4 * 8 + b * 8) + b(4 + b)) = 5
((32 + 8b) + b(4 + b)) = 5
(32 + 8b + (4 * b + b * b)) = 5
(32 + 8b + (4b + b2)) = 5

Combine like terms: 8b + 4b = 12b
(32 + 12b + b2) = 5

Solving
32 + 12b + b2 = 5

Solving for variable 'b'.

Reorder the terms:
32 + -5 + 12b + b2 = 5 + -5

Combine like terms: 32 + -5 = 27
27 + 12b + b2 = 5 + -5

Combine like terms: 5 + -5 = 0
27 + 12b + b2 = 0

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

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

Simplifying
9 + b = 0

Solving
9 + b = 0

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

Add '-9' to each side of the equation.
9 + -9 + b = 0 + -9

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

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

Simplifying
b = -9
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 = {-9, -3}