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Simplifying 6r3 = 15r2 + -6r Reorder the terms: 6r3 = -6r + 15r2 Solving 6r3 = -6r + 15r2 Solving for variable 'r'. Reorder the terms: 6r + -15r2 + 6r3 = -6r + 15r2 + 6r + -15r2 Reorder the terms: 6r + -15r2 + 6r3 = -6r + 6r + 15r2 + -15r2 Combine like terms: -6r + 6r = 0 6r + -15r2 + 6r3 = 0 + 15r2 + -15r2 6r + -15r2 + 6r3 = 15r2 + -15r2 Combine like terms: 15r2 + -15r2 = 0 6r + -15r2 + 6r3 = 0 Factor out the Greatest Common Factor (GCF), '3r'. 3r(2 + -5r + 2r2) = 0 Factor a trinomial. 3r((1 + -2r)(2 + -1r)) = 0 Ignore the factor 3.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 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 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 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Subproblem 3
Set the factor '(2 + -1r)' equal to zero and attempt to solve: Simplifying 2 + -1r = 0 Solving 2 + -1r = 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 + -1r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1r = 0 + -2 -1r = 0 + -2 Combine like terms: 0 + -2 = -2 -1r = -2 Divide each side by '-1'. r = 2 Simplifying r = 2Solution
r = {0, 0.5, 2}
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