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Simplifying -8(3r2 + -9r) + 3(7r2 + 7r) = 0 Reorder the terms: -8(-9r + 3r2) + 3(7r2 + 7r) = 0 (-9r * -8 + 3r2 * -8) + 3(7r2 + 7r) = 0 (72r + -24r2) + 3(7r2 + 7r) = 0 Reorder the terms: 72r + -24r2 + 3(7r + 7r2) = 0 72r + -24r2 + (7r * 3 + 7r2 * 3) = 0 72r + -24r2 + (21r + 21r2) = 0 Reorder the terms: 72r + 21r + -24r2 + 21r2 = 0 Combine like terms: 72r + 21r = 93r 93r + -24r2 + 21r2 = 0 Combine like terms: -24r2 + 21r2 = -3r2 93r + -3r2 = 0 Solving 93r + -3r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(31 + -1r) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'r' equal to zero and attempt to solve: Simplifying r = 0 Solving r = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r = 0Subproblem 2
Set the factor '(31 + -1r)' equal to zero and attempt to solve: Simplifying 31 + -1r = 0 Solving 31 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -1r = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -1r = 0 + -31 -1r = 0 + -31 Combine like terms: 0 + -31 = -31 -1r = -31 Divide each side by '-1'. r = 31 Simplifying r = 31Solution
r = {0, 31}
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