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Simplifying 2r(9r + -2)(2r + -1) = 0 Reorder the terms: 2r(-2 + 9r)(2r + -1) = 0 Reorder the terms: 2r(-2 + 9r)(-1 + 2r) = 0 Multiply (-2 + 9r) * (-1 + 2r) 2r(-2(-1 + 2r) + 9r * (-1 + 2r)) = 0 2r((-1 * -2 + 2r * -2) + 9r * (-1 + 2r)) = 0 2r((2 + -4r) + 9r * (-1 + 2r)) = 0 2r(2 + -4r + (-1 * 9r + 2r * 9r)) = 0 2r(2 + -4r + (-9r + 18r2)) = 0 Combine like terms: -4r + -9r = -13r 2r(2 + -13r + 18r2) = 0 (2 * 2r + -13r * 2r + 18r2 * 2r) = 0 (4r + -26r2 + 36r3) = 0 Solving 4r + -26r2 + 36r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(2 + -13r + 18r2) = 0 Factor a trinomial. 2r((2 + -9r)(1 + -2r)) = 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 '(2 + -9r)' equal to zero and attempt to solve: Simplifying 2 + -9r = 0 Solving 2 + -9r = 0 Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -9r = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -9r = 0 + -2 -9r = 0 + -2 Combine like terms: 0 + -2 = -2 -9r = -2 Divide each side by '-9'. r = 0.2222222222 Simplifying r = 0.2222222222Subproblem 3
Set the factor '(1 + -2r)' equal to zero and attempt to solve: Simplifying 1 + -2r = 0 Solving 1 + -2r = 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 + -2r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2r = 0 + -1 -2r = 0 + -1 Combine like terms: 0 + -1 = -1 -2r = -1 Divide each side by '-2'. r = 0.5 Simplifying r = 0.5Solution
r = {0, 0.2222222222, 0.5}
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