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Simplifying 5r(9r + -5)(5r + -1) = 0 Reorder the terms: 5r(-5 + 9r)(5r + -1) = 0 Reorder the terms: 5r(-5 + 9r)(-1 + 5r) = 0 Multiply (-5 + 9r) * (-1 + 5r) 5r(-5(-1 + 5r) + 9r * (-1 + 5r)) = 0 5r((-1 * -5 + 5r * -5) + 9r * (-1 + 5r)) = 0 5r((5 + -25r) + 9r * (-1 + 5r)) = 0 5r(5 + -25r + (-1 * 9r + 5r * 9r)) = 0 5r(5 + -25r + (-9r + 45r2)) = 0 Combine like terms: -25r + -9r = -34r 5r(5 + -34r + 45r2) = 0 (5 * 5r + -34r * 5r + 45r2 * 5r) = 0 (25r + -170r2 + 225r3) = 0 Solving 25r + -170r2 + 225r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5r'. 5r(5 + -34r + 45r2) = 0 Factor a trinomial. 5r((1 + -5r)(5 + -9r)) = 0 Ignore the factor 5.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 '(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 = 0.2Subproblem 3
Set the factor '(5 + -9r)' equal to zero and attempt to solve: Simplifying 5 + -9r = 0 Solving 5 + -9r = 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 + -9r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9r = 0 + -5 -9r = 0 + -5 Combine like terms: 0 + -5 = -5 -9r = -5 Divide each side by '-9'. r = 0.5555555556 Simplifying r = 0.5555555556Solution
r = {0, 0.2, 0.5555555556}
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