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Simplifying 14r3 + -33r2 + 18r = 0 Reorder the terms: 18r + -33r2 + 14r3 = 0 Solving 18r + -33r2 + 14r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(18 + -33r + 14r2) = 0 Factor a trinomial. r((6 + -7r)(3 + -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 '(6 + -7r)' equal to zero and attempt to solve: Simplifying 6 + -7r = 0 Solving 6 + -7r = 0 Move all terms containing r to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7r = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7r = 0 + -6 -7r = 0 + -6 Combine like terms: 0 + -6 = -6 -7r = -6 Divide each side by '-7'. r = 0.8571428571 Simplifying r = 0.8571428571Subproblem 3
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, 0.8571428571, 1.5}
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