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Simplifying 5r3 + -6r = 13r2 Reorder the terms: -6r + 5r3 = 13r2 Solving -6r + 5r3 = 13r2 Solving for variable 'r'. Reorder the terms: -6r + -13r2 + 5r3 = 13r2 + -13r2 Combine like terms: 13r2 + -13r2 = 0 -6r + -13r2 + 5r3 = 0 Factor out the Greatest Common Factor (GCF), 'r'. r(-6 + -13r + 5r2) = 0 Factor a trinomial. r((-2 + -5r)(3 + -1r)) = 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 '(-2 + -5r)' equal to zero and attempt to solve: Simplifying -2 + -5r = 0 Solving -2 + -5r = 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 + -5r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5r = 0 + 2 -5r = 0 + 2 Combine like terms: 0 + 2 = 2 -5r = 2 Divide each side by '-5'. r = -0.4 Simplifying r = -0.4Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {0, -0.4, 3}
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