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Simplifying 3r(4r + 5)(7r + 3) = 0 Reorder the terms: 3r(5 + 4r)(7r + 3) = 0 Reorder the terms: 3r(5 + 4r)(3 + 7r) = 0 Multiply (5 + 4r) * (3 + 7r) 3r(5(3 + 7r) + 4r * (3 + 7r)) = 0 3r((3 * 5 + 7r * 5) + 4r * (3 + 7r)) = 0 3r((15 + 35r) + 4r * (3 + 7r)) = 0 3r(15 + 35r + (3 * 4r + 7r * 4r)) = 0 3r(15 + 35r + (12r + 28r2)) = 0 Combine like terms: 35r + 12r = 47r 3r(15 + 47r + 28r2) = 0 (15 * 3r + 47r * 3r + 28r2 * 3r) = 0 (45r + 141r2 + 84r3) = 0 Solving 45r + 141r2 + 84r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(15 + 47r + 28r2) = 0 Factor a trinomial. 3r((5 + 4r)(3 + 7r)) = 0 Ignore the factor 3.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 + 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 = -1.25Subproblem 3
Set the factor '(3 + 7r)' equal to zero and attempt to solve: Simplifying 3 + 7r = 0 Solving 3 + 7r = 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 + 7r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7r = 0 + -3 7r = 0 + -3 Combine like terms: 0 + -3 = -3 7r = -3 Divide each side by '7'. r = -0.4285714286 Simplifying r = -0.4285714286Solution
r = {0, -1.25, -0.4285714286}
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