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Simplifying 2r(3r + 5)(4r + 5) = 0 Reorder the terms: 2r(5 + 3r)(4r + 5) = 0 Reorder the terms: 2r(5 + 3r)(5 + 4r) = 0 Multiply (5 + 3r) * (5 + 4r) 2r(5(5 + 4r) + 3r * (5 + 4r)) = 0 2r((5 * 5 + 4r * 5) + 3r * (5 + 4r)) = 0 2r((25 + 20r) + 3r * (5 + 4r)) = 0 2r(25 + 20r + (5 * 3r + 4r * 3r)) = 0 2r(25 + 20r + (15r + 12r2)) = 0 Combine like terms: 20r + 15r = 35r 2r(25 + 35r + 12r2) = 0 (25 * 2r + 35r * 2r + 12r2 * 2r) = 0 (50r + 70r2 + 24r3) = 0 Solving 50r + 70r2 + 24r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(25 + 35r + 12r2) = 0 Factor a trinomial. 2r((5 + 3r)(5 + 4r)) = 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 '(5 + 3r)' equal to zero and attempt to solve: Simplifying 5 + 3r = 0 Solving 5 + 3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3r = 0 + -5 3r = 0 + -5 Combine like terms: 0 + -5 = -5 3r = -5 Divide each side by '3'. r = -1.666666667 Simplifying r = -1.666666667Subproblem 3
Set the factor '(5 + 4r)' equal to zero and attempt to solve: Simplifying 5 + 4r = 0 Solving 5 + 4r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4r = 0 + -5 4r = 0 + -5 Combine like terms: 0 + -5 = -5 4r = -5 Divide each side by '4'. r = -1.25 Simplifying r = -1.25Solution
r = {0, -1.666666667, -1.25}
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