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Simplifying 11r + -2r + 5 = -3r + 5 + 8r2 Reorder the terms: 5 + 11r + -2r = -3r + 5 + 8r2 Combine like terms: 11r + -2r = 9r 5 + 9r = -3r + 5 + 8r2 Reorder the terms: 5 + 9r = 5 + -3r + 8r2 Add '-5' to each side of the equation. 5 + -5 + 9r = 5 + -3r + -5 + 8r2 Combine like terms: 5 + -5 = 0 0 + 9r = 5 + -3r + -5 + 8r2 9r = 5 + -3r + -5 + 8r2 Reorder the terms: 9r = 5 + -5 + -3r + 8r2 Combine like terms: 5 + -5 = 0 9r = 0 + -3r + 8r2 9r = -3r + 8r2 Solving 9r = -3r + 8r2 Solving for variable 'r'. Combine like terms: 9r + 3r = 12r 12r + -8r2 = -3r + 8r2 + 3r + -8r2 Reorder the terms: 12r + -8r2 = -3r + 3r + 8r2 + -8r2 Combine like terms: -3r + 3r = 0 12r + -8r2 = 0 + 8r2 + -8r2 12r + -8r2 = 8r2 + -8r2 Combine like terms: 8r2 + -8r2 = 0 12r + -8r2 = 0 Factor out the Greatest Common Factor (GCF), '4r'. 4r(3 + -2r) = 0 Ignore the factor 4.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 '(3 + -2r)' equal to zero and attempt to solve: Simplifying 3 + -2r = 0 Solving 3 + -2r = 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 + -2r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r = 0 + -3 -2r = 0 + -3 Combine like terms: 0 + -3 = -3 -2r = -3 Divide each side by '-2'. r = 1.5 Simplifying r = 1.5Solution
r = {0, 1.5}
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