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Simplifying 5r2 + -44r + 120 = 11r Reorder the terms: 120 + -44r + 5r2 = 11r Solving 120 + -44r + 5r2 = 11r Solving for variable 'r'. Reorder the terms: 120 + -44r + -11r + 5r2 = 11r + -11r Combine like terms: -44r + -11r = -55r 120 + -55r + 5r2 = 11r + -11r Combine like terms: 11r + -11r = 0 120 + -55r + 5r2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(24 + -11r + r2) = 0 Factor a trinomial. 5((3 + -1r)(8 + -1r)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8Solution
r = {3, 8}
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