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Simplifying 36r3 + -30r2 + 4r = 0 Reorder the terms: 4r + -30r2 + 36r3 = 0 Solving 4r + -30r2 + 36r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(2 + -15r + 18r2) = 0 Factor a trinomial. 2r((1 + -6r)(2 + -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 = 0Subproblem 2
Set the factor '(1 + -6r)' equal to zero and attempt to solve: Simplifying 1 + -6r = 0 Solving 1 + -6r = 0 Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6r = 0 + -1 -6r = 0 + -1 Combine like terms: 0 + -1 = -1 -6r = -1 Divide each side by '-6'. r = 0.1666666667 Simplifying r = 0.1666666667Subproblem 3
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 = 0.6666666667Solution
r = {0, 0.1666666667, 0.6666666667}
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