b^2=24-5b

Solution for b^2=24-5b equation:

Simplifying
b2 = 24 + -5b

Solving
b2 = 24 + -5b

Solving for variable 'b'.

Reorder the terms:
-24 + 5b + b2 = 24 + -5b + -24 + 5b

Reorder the terms:
-24 + 5b + b2 = 24 + -24 + -5b + 5b

Combine like terms: 24 + -24 = 0
-24 + 5b + b2 = 0 + -5b + 5b
-24 + 5b + b2 = -5b + 5b

Combine like terms: -5b + 5b = 0
-24 + 5b + b2 = 0

Factor a trinomial.
(-8 + -1b)(3 + -1b) = 0

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

Simplifying
-8 + -1b = 0

Solving
-8 + -1b = 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 + -1b = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1b = 0 + 8
-1b = 0 + 8

Combine like terms: 0 + 8 = 8
-1b = 8

Divide each side by '-1'.
b = -8

Simplifying
b = -8
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-8, 3}