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Simplifying 12r3 + -5r2 + -2r = 0 Reorder the terms: -2r + -5r2 + 12r3 = 0 Solving -2r + -5r2 + 12r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-2 + -5r + 12r2) = 0 Factor a trinomial. r((-1 + -4r)(2 + -3r)) = 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 '(-1 + -4r)' equal to zero and attempt to solve: Simplifying -1 + -4r = 0 Solving -1 + -4r = 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 + -4r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4r = 0 + 1 -4r = 0 + 1 Combine like terms: 0 + 1 = 1 -4r = 1 Divide each side by '-4'. r = -0.25 Simplifying r = -0.25Subproblem 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, -0.25, 0.6666666667}
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