Simplifying
b^{2} + 12b + 35 = 0
Reorder the terms:
35 + 12b + b^{2} = 0
Solving
35 + 12b + b^{2} = 0
Solving for variable 'b'.
Factor a trinomial.
(7 + b)(5 + b) = 0
#### Subproblem 1

Set the factor '(7 + b)' equal to zero and attempt to solve:
Simplifying
7 + b = 0
Solving
7 + b = 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 + b = 0 + -7
Combine like terms: 7 + -7 = 0
0 + b = 0 + -7
b = 0 + -7
Combine like terms: 0 + -7 = -7
b = -7
Simplifying
b = -7
#### Subproblem 2

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#### Solution

b = {-7, -5}