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Simplifying 6r^{2}+ 10r = 0 Reorder the terms: 10r + 6r^{2}= 0 Solving 10r + 6r^{2}= 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(5 + 3r) = 0 Ignore the factor 2.## 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 = 0## Subproblem 2

Set the factor '(5 + 3r)' equal to zero and attempt to solve: Simplifying 5 + 3r = 0 Solving 5 + 3r = 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 + 3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3r = 0 + -5 3r = 0 + -5 Combine like terms: 0 + -5 = -5 3r = -5 Divide each side by '3'. r = -1.666666667 Simplifying r = -1.666666667## Solution

r = {0, -1.666666667}

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