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Simplifying 6r2 + 240 = 78r Reorder the terms: 240 + 6r2 = 78r Solving 240 + 6r2 = 78r Solving for variable 'r'. Reorder the terms: 240 + -78r + 6r2 = 78r + -78r Combine like terms: 78r + -78r = 0 240 + -78r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(40 + -13r + r2) = 0 Factor a trinomial. 6((5 + -1r)(8 + -1r)) = 0 Ignore the factor 6.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 '(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 = {5, 8}
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