12r^2-132r+360=0

Solution for 12r^2-132r+360=0 equation:

Simplifying
12r2 + -132r + 360 = 0

Reorder the terms:
360 + -132r + 12r2 = 0

Solving
360 + -132r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '12'.
12(30 + -11r + r2) = 0

Factor a trinomial.
12((5 + -1r)(6 + -1r)) = 0

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

Simplifying
5 + -1r = 0

Solving
5 + -1r = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r = 0 + -5

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

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

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

Simplifying
r = 5
Subproblem 2
Set the factor '(6 + -1r)' equal to zero and attempt to solve:

Simplifying
6 + -1r = 0

Solving
6 + -1r = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1r = 0 + -6

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

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

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

Simplifying
r = 6
Solution
r = {5, 6}