b^2+14b=-45

Solution for b^2+14b=-45 equation:

Simplifying
b2 + 14b = -45

Reorder the terms:
14b + b2 = -45

Solving
14b + b2 = -45

Solving for variable 'b'.

Reorder the terms:
45 + 14b + b2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 14b + b2 = 0

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

Subproblem 1
Set the factor '(9 + b)' equal to zero and attempt to solve:

Simplifying
9 + b = 0

Solving
9 + b = 0

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

Add '-9' to each side of the equation.
9 + -9 + b = 0 + -9

Combine like terms: 9 + -9 = 0
0 + b = 0 + -9
b = 0 + -9

Combine like terms: 0 + -9 = -9
b = -9

Simplifying
b = -9
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 = {-9, -5}