12b(b-3)=120

Solution for 12b(b-3)=120 equation:

Simplifying
12b(b + -3) = 120

Reorder the terms:
12b(-3 + b) = 120
(-3 * 12b + b * 12b) = 120
(-36b + 12b2) = 120

Solving
-36b + 12b2 = 120

Solving for variable 'b'.

Reorder the terms:
-120 + -36b + 12b2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + -36b + 12b2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(-10 + -3b + b2) = 0

Factor a trinomial.
12((-2 + -1b)(5 + -1b)) = 0

Ignore the factor 12.
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 '(5 + -1b)' equal to zero and attempt to solve:

Simplifying
5 + -1b = 0

Solving
5 + -1b = 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 + -1b = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1b = 0 + -5
-1b = 0 + -5

Combine like terms: 0 + -5 = -5
-1b = -5

Divide each side by '-1'.
b = 5

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