b^2=-35-12b

Solution for b^2=-35-12b equation:

Simplifying
b2 = -35 + -12b

Solving
b2 = -35 + -12b

Solving for variable 'b'.

Reorder the terms:
35 + 12b + b2 = -35 + -12b + 35 + 12b

Reorder the terms:
35 + 12b + b2 = -35 + 35 + -12b + 12b

Combine like terms: -35 + 35 = 0
35 + 12b + b2 = 0 + -12b + 12b
35 + 12b + b2 = -12b + 12b

Combine like terms: -12b + 12b = 0
35 + 12b + b2 = 0

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}