b^2+13b+31=b-5

Solution for b^2+13b+31=b-5 equation:

Simplifying
b2 + 13b + 31 = b + -5

Reorder the terms:
31 + 13b + b2 = b + -5

Reorder the terms:
31 + 13b + b2 = -5 + b

Solving
31 + 13b + b2 = -5 + b

Solving for variable 'b'.

Reorder the terms:
31 + 5 + 13b + -1b + b2 = -5 + b + 5 + -1b

Combine like terms: 31 + 5 = 36
36 + 13b + -1b + b2 = -5 + b + 5 + -1b

Combine like terms: 13b + -1b = 12b
36 + 12b + b2 = -5 + b + 5 + -1b

Reorder the terms:
36 + 12b + b2 = -5 + 5 + b + -1b

Combine like terms: -5 + 5 = 0
36 + 12b + b2 = 0 + b + -1b
36 + 12b + b2 = b + -1b

Combine like terms: b + -1b = 0
36 + 12b + b2 = 0

Factor a trinomial.
(6 + b)(6 + b) = 0

Subproblem 1
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

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

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Subproblem 2
Set the factor '(6 + b)' equal to zero and attempt to solve:

Simplifying
6 + b = 0

Solving
6 + b = 0

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

Add '-6' to each side of the equation.
6 + -6 + b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + b = 0 + -6
b = 0 + -6

Combine like terms: 0 + -6 = -6
b = -6

Simplifying
b = -6
Solution
b = {-6, -6}