5r^2-44r+120=-30+11r

Solution for 5r^2-44r+120=-30+11r equation:

Simplifying
5r2 + -44r + 120 = -30 + 11r

Reorder the terms:
120 + -44r + 5r2 = -30 + 11r

Solving
120 + -44r + 5r2 = -30 + 11r

Solving for variable 'r'.

Reorder the terms:
120 + 30 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r

Combine like terms: 120 + 30 = 150
150 + -44r + -11r + 5r2 = -30 + 11r + 30 + -11r

Combine like terms: -44r + -11r = -55r
150 + -55r + 5r2 = -30 + 11r + 30 + -11r

Reorder the terms:
150 + -55r + 5r2 = -30 + 30 + 11r + -11r

Combine like terms: -30 + 30 = 0
150 + -55r + 5r2 = 0 + 11r + -11r
150 + -55r + 5r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
150 + -55r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + -11r + r2) = 0

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

Ignore the factor 5.
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}