b^2=-10-7b

Solution for b^2=-10-7b equation:

Simplifying
b2 = -10 + -7b

Solving
b2 = -10 + -7b

Solving for variable 'b'.

Reorder the terms:
10 + 7b + b2 = -10 + -7b + 10 + 7b

Reorder the terms:
10 + 7b + b2 = -10 + 10 + -7b + 7b

Combine like terms: -10 + 10 = 0
10 + 7b + b2 = 0 + -7b + 7b
10 + 7b + b2 = -7b + 7b

Combine like terms: -7b + 7b = 0
10 + 7b + b2 = 0

Factor a trinomial.
(5 + b)(2 + b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + b)' equal to zero and attempt to solve:

Simplifying
2 + b = 0

Solving
2 + b = 0

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

Add '-2' to each side of the equation.
2 + -2 + b = 0 + -2

Combine like terms: 2 + -2 = 0
0 + b = 0 + -2
b = 0 + -2

Combine like terms: 0 + -2 = -2
b = -2

Simplifying
b = -2
Solution
b = {-5, -2}