b^2=-21-10b

Solution for b^2=-21-10b equation:

Simplifying
b2 = -21 + -10b

Solving
b2 = -21 + -10b

Solving for variable 'b'.

Reorder the terms:
21 + 10b + b2 = -21 + -10b + 21 + 10b

Reorder the terms:
21 + 10b + b2 = -21 + 21 + -10b + 10b

Combine like terms: -21 + 21 = 0
21 + 10b + b2 = 0 + -10b + 10b
21 + 10b + b2 = -10b + 10b

Combine like terms: -10b + 10b = 0
21 + 10b + b2 = 0

Factor a trinomial.
(7 + b)(3 + b) = 0

Subproblem 1
Set the factor '(7 + b)' equal to zero and attempt to solve:

Simplifying
7 + b = 0

Solving
7 + b = 0

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

Add '-7' to each side of the equation.
7 + -7 + b = 0 + -7

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

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

Simplifying
b = -7
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 0

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

Add '-3' to each side of the equation.
3 + -3 + b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + b = 0 + -3
b = 0 + -3

Combine like terms: 0 + -3 = -3
b = -3

Simplifying
b = -3
Solution
b = {-7, -3}