5r^2-44r+120=-30+111r

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Solution for 5r^2-44r+120=-30+111r equation: 


Simplifying
5r2 + -44r + 120 = -30 + 111r

Reorder the terms:
120 + -44r + 5r2 = -30 + 111r

Solving
120 + -44r + 5r2 = -30 + 111r

Solving for variable 'r'.

Reorder the terms:
120 + 30 + -44r + -111r + 5r2 = -30 + 111r + 30 + -111r

Combine like terms: 120 + 30 = 150
150 + -44r + -111r + 5r2 = -30 + 111r + 30 + -111r

Combine like terms: -44r + -111r = -155r
150 + -155r + 5r2 = -30 + 111r + 30 + -111r

Reorder the terms:
150 + -155r + 5r2 = -30 + 30 + 111r + -111r

Combine like terms: -30 + 30 = 0
150 + -155r + 5r2 = 0 + 111r + -111r
150 + -155r + 5r2 = 111r + -111r

Combine like terms: 111r + -111r = 0
150 + -155r + 5r2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(30 + -31r + r2) = 0

Factor a trinomial.
5((1 + -1r)(30 + -1r)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1r = 0

Solving
1 + -1r = 0

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

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

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

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

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

Simplifying
r = 1

Subproblem 2
Set the factor '(30 + -1r)' equal to zero and attempt to solve:

Simplifying
30 + -1r = 0

Solving
30 + -1r = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1r = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1r = 0 + -30
-1r = 0 + -30

Combine like terms: 0 + -30 = -30
-1r = -30

Divide each side by '-1'.
r = 30

Simplifying
r = 30
Solution
r = {1, 30}

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