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Simplifying (5r2) + -1(44r) + 120 = -30 + 11r Remove parenthesis around (44r) (5r2) + -1 * 44r + 120 = -30 + 11r Multiply -1 * 44 (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 = 5Subproblem 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 = 6Solution
r = {5, 6}
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