b^2=-10b-24

Solution for b^2=-10b-24 equation:

Simplifying
b2 = -10b + -24

Reorder the terms:
b2 = -24 + -10b

Solving
b2 = -24 + -10b

Solving for variable 'b'.

Reorder the terms:
24 + 10b + b2 = -24 + -10b + 24 + 10b

Reorder the terms:
24 + 10b + b2 = -24 + 24 + -10b + 10b

Combine like terms: -24 + 24 = 0
24 + 10b + b2 = 0 + -10b + 10b
24 + 10b + b2 = -10b + 10b

Combine like terms: -10b + 10b = 0
24 + 10b + b2 = 0

Factor a trinomial.
(6 + b)(4 + 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 '(4 + b)' equal to zero and attempt to solve:

Simplifying
4 + b = 0

Solving
4 + b = 0

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

Add '-4' to each side of the equation.
4 + -4 + b = 0 + -4

Combine like terms: 4 + -4 = 0
0 + b = 0 + -4
b = 0 + -4

Combine like terms: 0 + -4 = -4
b = -4

Simplifying
b = -4
Solution
b = {-6, -4}