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Simplifying 3r(8r + -3)(3r + -1) = 0 Reorder the terms: 3r(-3 + 8r)(3r + -1) = 0 Reorder the terms: 3r(-3 + 8r)(-1 + 3r) = 0 Multiply (-3 + 8r) * (-1 + 3r) 3r(-3(-1 + 3r) + 8r * (-1 + 3r)) = 0 3r((-1 * -3 + 3r * -3) + 8r * (-1 + 3r)) = 0 3r((3 + -9r) + 8r * (-1 + 3r)) = 0 3r(3 + -9r + (-1 * 8r + 3r * 8r)) = 0 3r(3 + -9r + (-8r + 24r2)) = 0 Combine like terms: -9r + -8r = -17r 3r(3 + -17r + 24r2) = 0 (3 * 3r + -17r * 3r + 24r2 * 3r) = 0 (9r + -51r2 + 72r3) = 0 Solving 9r + -51r2 + 72r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(3 + -17r + 24r2) = 0 Factor a trinomial. 3r((1 + -3r)(3 + -8r)) = 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 '(1 + -3r)' equal to zero and attempt to solve: Simplifying 1 + -3r = 0 Solving 1 + -3r = 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 + -3r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3r = 0 + -1 -3r = 0 + -1 Combine like terms: 0 + -1 = -1 -3r = -1 Divide each side by '-3'. r = 0.3333333333 Simplifying r = 0.3333333333Subproblem 3
Set the factor '(3 + -8r)' equal to zero and attempt to solve: Simplifying 3 + -8r = 0 Solving 3 + -8r = 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 + -8r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8r = 0 + -3 -8r = 0 + -3 Combine like terms: 0 + -3 = -3 -8r = -3 Divide each side by '-8'. r = 0.375 Simplifying r = 0.375Solution
r = {0, 0.3333333333, 0.375}
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