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Simplifying 8r(3r + -1)(r + 2) = 0 Reorder the terms: 8r(-1 + 3r)(r + 2) = 0 Reorder the terms: 8r(-1 + 3r)(2 + r) = 0 Multiply (-1 + 3r) * (2 + r) 8r(-1(2 + r) + 3r * (2 + r)) = 0 8r((2 * -1 + r * -1) + 3r * (2 + r)) = 0 8r((-2 + -1r) + 3r * (2 + r)) = 0 8r(-2 + -1r + (2 * 3r + r * 3r)) = 0 8r(-2 + -1r + (6r + 3r2)) = 0 Combine like terms: -1r + 6r = 5r 8r(-2 + 5r + 3r2) = 0 (-2 * 8r + 5r * 8r + 3r2 * 8r) = 0 (-16r + 40r2 + 24r3) = 0 Solving -16r + 40r2 + 24r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '8r'. 8r(-2 + 5r + 3r2) = 0 Factor a trinomial. 8r((-2 + -1r)(1 + -3r)) = 0 Ignore the factor 8.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 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 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 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 3
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 = 0.3333333333Solution
r = {0, -2, 0.3333333333}
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