(b+5)(b+1)=12

Solution for (b+5)(b+1)=12 equation:

Simplifying
(b + 5)(b + 1) = 12

Reorder the terms:
(5 + b)(b + 1) = 12

Reorder the terms:
(5 + b)(1 + b) = 12

Multiply (5 + b) * (1 + b)
(5(1 + b) + b(1 + b)) = 12
((1 * 5 + b * 5) + b(1 + b)) = 12
((5 + 5b) + b(1 + b)) = 12
(5 + 5b + (1 * b + b * b)) = 12
(5 + 5b + (1b + b2)) = 12

Combine like terms: 5b + 1b = 6b
(5 + 6b + b2) = 12

Solving
5 + 6b + b2 = 12

Solving for variable 'b'.

Reorder the terms:
5 + -12 + 6b + b2 = 12 + -12

Combine like terms: 5 + -12 = -7
-7 + 6b + b2 = 12 + -12

Combine like terms: 12 + -12 = 0
-7 + 6b + b2 = 0

Factor a trinomial.
(-7 + -1b)(1 + -1b) = 0

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

Simplifying
-7 + -1b = 0

Solving
-7 + -1b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1b = 0 + 7
-1b = 0 + 7

Combine like terms: 0 + 7 = 7
-1b = 7

Divide each side by '-1'.
b = -7

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

Simplifying
1 + -1b = 0

Solving
1 + -1b = 0

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

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

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

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

Divide each side by '-1'.
b = 1

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