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Simplifying 9r3 + -21r2 + -8r = 0 Reorder the terms: -8r + -21r2 + 9r3 = 0 Solving -8r + -21r2 + 9r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-8 + -21r + 9r2) = 0 Factor a trinomial. r((-1 + -3r)(8 + -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 + -3r)' equal to zero and attempt to solve: Simplifying -1 + -3r = 0 Solving -1 + -3r = 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 + -3r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3r = 0 + 1 -3r = 0 + 1 Combine like terms: 0 + 1 = 1 -3r = 1 Divide each side by '-3'. r = -0.3333333333 Simplifying r = -0.3333333333Subproblem 3
Set the factor '(8 + -3r)' equal to zero and attempt to solve: Simplifying 8 + -3r = 0 Solving 8 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3r = 0 + -8 -3r = 0 + -8 Combine like terms: 0 + -8 = -8 -3r = -8 Divide each side by '-3'. r = 2.666666667 Simplifying r = 2.666666667Solution
r = {0, -0.3333333333, 2.666666667}
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