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Simplifying 18r3 + -33r2 + 14r = 0 Reorder the terms: 14r + -33r2 + 18r3 = 0 Solving 14r + -33r2 + 18r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(14 + -33r + 18r2) = 0 Factor a trinomial. r((2 + -3r)(7 + -6r)) = 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 '(2 + -3r)' equal to zero and attempt to solve: Simplifying 2 + -3r = 0 Solving 2 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3r = 0 + -2 -3r = 0 + -2 Combine like terms: 0 + -2 = -2 -3r = -2 Divide each side by '-3'. r = 0.6666666667 Simplifying r = 0.6666666667Subproblem 3
Set the factor '(7 + -6r)' equal to zero and attempt to solve: Simplifying 7 + -6r = 0 Solving 7 + -6r = 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 + -6r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6r = 0 + -7 -6r = 0 + -7 Combine like terms: 0 + -7 = -7 -6r = -7 Divide each side by '-6'. r = 1.166666667 Simplifying r = 1.166666667Solution
r = {0, 0.6666666667, 1.166666667}
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