3r^2-12r-180=0

Solution for 3r^2-12r-180=0 equation:

Simplifying
3r2 + -12r + -180 = 0

Reorder the terms:
-180 + -12r + 3r2 = 0

Solving
-180 + -12r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + -4r + r2) = 0

Factor a trinomial.
3((-6 + -1r)(10 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {-6, 10}