b^2-2b=3b+24

Solution for b^2-2b=3b+24 equation:

Simplifying
b2 + -2b = 3b + 24

Reorder the terms:
-2b + b2 = 3b + 24

Reorder the terms:
-2b + b2 = 24 + 3b

Solving
-2b + b2 = 24 + 3b

Solving for variable 'b'.

Reorder the terms:
-24 + -2b + -3b + b2 = 24 + 3b + -24 + -3b

Combine like terms: -2b + -3b = -5b
-24 + -5b + b2 = 24 + 3b + -24 + -3b

Reorder the terms:
-24 + -5b + b2 = 24 + -24 + 3b + -3b

Combine like terms: 24 + -24 = 0
-24 + -5b + b2 = 0 + 3b + -3b
-24 + -5b + b2 = 3b + -3b

Combine like terms: 3b + -3b = 0
-24 + -5b + b2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
b = {-3, 8}