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Simplifying 6r2 = 15 + 27r Solving 6r2 = 15 + 27r Solving for variable 'r'. Reorder the terms: -15 + -27r + 6r2 = 15 + 27r + -15 + -27r Reorder the terms: -15 + -27r + 6r2 = 15 + -15 + 27r + -27r Combine like terms: 15 + -15 = 0 -15 + -27r + 6r2 = 0 + 27r + -27r -15 + -27r + 6r2 = 27r + -27r Combine like terms: 27r + -27r = 0 -15 + -27r + 6r2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + -9r + 2r2) = 0 Factor a trinomial. 3((-1 + -2r)(5 + -1r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -2r)' equal to zero and attempt to solve: Simplifying -1 + -2r = 0 Solving -1 + -2r = 0 Move all terms containing r to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2r = 0 + 1 -2r = 0 + 1 Combine like terms: 0 + 1 = 1 -2r = 1 Divide each side by '-2'. r = -0.5 Simplifying r = -0.5Subproblem 2
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 = 5Solution
r = {-0.5, 5}
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