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Simplifying 2r(2r + 6) + r(9r + 8) = 0 Reorder the terms: 2r(6 + 2r) + r(9r + 8) = 0 (6 * 2r + 2r * 2r) + r(9r + 8) = 0 (12r + 4r2) + r(9r + 8) = 0 Reorder the terms: 12r + 4r2 + r(8 + 9r) = 0 12r + 4r2 + (8 * r + 9r * r) = 0 12r + 4r2 + (8r + 9r2) = 0 Reorder the terms: 12r + 8r + 4r2 + 9r2 = 0 Combine like terms: 12r + 8r = 20r 20r + 4r2 + 9r2 = 0 Combine like terms: 4r2 + 9r2 = 13r2 20r + 13r2 = 0 Solving 20r + 13r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(20 + 13r) = 0Subproblem 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 '(20 + 13r)' equal to zero and attempt to solve: Simplifying 20 + 13r = 0 Solving 20 + 13r = 0 Move all terms containing r to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + 13r = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 13r = 0 + -20 13r = 0 + -20 Combine like terms: 0 + -20 = -20 13r = -20 Divide each side by '13'. r = -1.538461538 Simplifying r = -1.538461538Solution
r = {0, -1.538461538}
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