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Simplifying 40r3 + 22r2 + -6r = 0 Reorder the terms: -6r + 22r2 + 40r3 = 0 Solving -6r + 22r2 + 40r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(-3 + 11r + 20r2) = 0 Factor a trinomial. 2r((-3 + -4r)(1 + -5r)) = 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 + -4r)' equal to zero and attempt to solve: Simplifying -3 + -4r = 0 Solving -3 + -4r = 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 + -4r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4r = 0 + 3 -4r = 0 + 3 Combine like terms: 0 + 3 = 3 -4r = 3 Divide each side by '-4'. r = -0.75 Simplifying r = -0.75Subproblem 3
Set the factor '(1 + -5r)' equal to zero and attempt to solve: Simplifying 1 + -5r = 0 Solving 1 + -5r = 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 + -5r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5r = 0 + -1 -5r = 0 + -1 Combine like terms: 0 + -1 = -1 -5r = -1 Divide each side by '-5'. r = 0.2 Simplifying r = 0.2Solution
r = {0, -0.75, 0.2}
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