b^2+13b+40=0

Solution for b^2+13b+40=0 equation:

Simplifying
b2 + 13b + 40 = 0

Reorder the terms:
40 + 13b + b2 = 0

Solving
40 + 13b + b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(8 + b)(5 + b) = 0

Subproblem 1
Set the factor '(8 + b)' equal to zero and attempt to solve:

Simplifying
8 + b = 0

Solving
8 + b = 0

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

Add '-8' to each side of the equation.
8 + -8 + b = 0 + -8

Combine like terms: 8 + -8 = 0
0 + b = 0 + -8
b = 0 + -8

Combine like terms: 0 + -8 = -8
b = -8

Simplifying
b = -8
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 = {-8, -5}