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Simplifying 6r3 + -31r2 + 35r = 0 Reorder the terms: 35r + -31r2 + 6r3 = 0 Solving 35r + -31r2 + 6r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(35 + -31r + 6r2) = 0 Factor a trinomial. r((5 + -3r)(7 + -2r)) = 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 '(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 = 1.666666667Subproblem 3
Set the factor '(7 + -2r)' equal to zero and attempt to solve: Simplifying 7 + -2r = 0 Solving 7 + -2r = 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 + -2r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2r = 0 + -7 -2r = 0 + -7 Combine like terms: 0 + -7 = -7 -2r = -7 Divide each side by '-2'. r = 3.5 Simplifying r = 3.5Solution
r = {0, 1.666666667, 3.5}
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