5r*r-44r+120=-30+11r

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


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

Multiply r * r
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}

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