9r^2-66r+120=0

Solution for 9r^2-66r+120=0 equation:

Simplifying
9r2 + -66r + 120 = 0

Reorder the terms:
120 + -66r + 9r2 = 0

Solving
120 + -66r + 9r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(40 + -22r + 3r2) = 0

Factor a trinomial.
3((10 + -3r)(4 + -1r)) = 0

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

Simplifying
10 + -3r = 0

Solving
10 + -3r = 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 + -3r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3r = 0 + -10
-3r = 0 + -10

Combine like terms: 0 + -10 = -10
-3r = -10

Divide each side by '-3'.
r = 3.333333333

Simplifying
r = 3.333333333
Subproblem 2
Set the factor '(4 + -1r)' equal to zero and attempt to solve:

Simplifying
4 + -1r = 0

Solving
4 + -1r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1r = 0 + -4
-1r = 0 + -4

Combine like terms: 0 + -4 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4
Solution
r = {3.333333333, 4}