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Simplifying 6r2 + -15r = 99 Reorder the terms: -15r + 6r2 = 99 Solving -15r + 6r2 = 99 Solving for variable 'r'. Reorder the terms: -99 + -15r + 6r2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + -15r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -5r + 2r2) = 0 Factor a trinomial. 3((-3 + -1r)(11 + -2r)) = 0 Ignore the factor 3.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 '(11 + -2r)' equal to zero and attempt to solve: Simplifying 11 + -2r = 0 Solving 11 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -2r = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -2r = 0 + -11 -2r = 0 + -11 Combine like terms: 0 + -11 = -11 -2r = -11 Divide each side by '-2'. r = 5.5 Simplifying r = 5.5Solution
r = {-3, 5.5}
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