b(b-3)=b+12

Solution for b(b-3)=b+12 equation:

Simplifying
b(b + -3) = b + 12

Reorder the terms:
b(-3 + b) = b + 12
(-3 * b + b * b) = b + 12
(-3b + b2) = b + 12

Reorder the terms:
-3b + b2 = 12 + b

Solving
-3b + b2 = 12 + b

Solving for variable 'b'.

Reorder the terms:
-12 + -3b + -1b + b2 = 12 + b + -12 + -1b

Combine like terms: -3b + -1b = -4b
-12 + -4b + b2 = 12 + b + -12 + -1b

Reorder the terms:
-12 + -4b + b2 = 12 + -12 + b + -1b

Combine like terms: 12 + -12 = 0
-12 + -4b + b2 = 0 + b + -1b
-12 + -4b + b2 = b + -1b

Combine like terms: b + -1b = 0
-12 + -4b + b2 = 0

Factor a trinomial.
(-2 + -1b)(6 + -1b) = 0

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 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 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 2
Set the factor '(6 + -1b)' equal to zero and attempt to solve:

Simplifying
6 + -1b = 0

Solving
6 + -1b = 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 + -1b = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1b = 0 + -6
-1b = 0 + -6

Combine like terms: 0 + -6 = -6
-1b = -6

Divide each side by '-1'.
b = 6

Simplifying
b = 6
Solution
b = {-2, 6}