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Simplifying 27r2 + 129r + 84 = 0 Reorder the terms: 84 + 129r + 27r2 = 0 Solving 84 + 129r + 27r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3'. 3(28 + 43r + 9r2) = 0 Factor a trinomial. 3((4 + r)(7 + 9r)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Subproblem 2
Set the factor '(7 + 9r)' equal to zero and attempt to solve: Simplifying 7 + 9r = 0 Solving 7 + 9r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 9r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9r = 0 + -7 9r = 0 + -7 Combine like terms: 0 + -7 = -7 9r = -7 Divide each side by '9'. r = -0.7777777778 Simplifying r = -0.7777777778Solution
r = {-4, -0.7777777778}
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