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Simplifying 4r3 + 11r2 + -3r = 0 Reorder the terms: -3r + 11r2 + 4r3 = 0 Solving -3r + 11r2 + 4r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r'. r(-3 + 11r + 4r2) = 0 Factor a trinomial. r((-3 + -1r)(1 + -4r)) = 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 '(-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 = -3Subproblem 3
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 = 0.25Solution
r = {0, -3, 0.25}
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