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Simplifying 12r3 + 10r2 + -12r = 0 Reorder the terms: -12r + 10r2 + 12r3 = 0 Solving -12r + 10r2 + 12r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(-6 + 5r + 6r2) = 0 Factor a trinomial. 2r((-3 + -2r)(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 '(-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 = -1.5Subproblem 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, -1.5, 0.6666666667}
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