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Simplifying 5r(4r + -1)(r + 2) = 0 Reorder the terms: 5r(-1 + 4r)(r + 2) = 0 Reorder the terms: 5r(-1 + 4r)(2 + r) = 0 Multiply (-1 + 4r) * (2 + r) 5r(-1(2 + r) + 4r * (2 + r)) = 0 5r((2 * -1 + r * -1) + 4r * (2 + r)) = 0 5r((-2 + -1r) + 4r * (2 + r)) = 0 5r(-2 + -1r + (2 * 4r + r * 4r)) = 0 5r(-2 + -1r + (8r + 4r2)) = 0 Combine like terms: -1r + 8r = 7r 5r(-2 + 7r + 4r2) = 0 (-2 * 5r + 7r * 5r + 4r2 * 5r) = 0 (-10r + 35r2 + 20r3) = 0 Solving -10r + 35r2 + 20r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5r'. 5r(-2 + 7r + 4r2) = 0 Factor a trinomial. 5r((-2 + -1r)(1 + -4r)) = 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 '(-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 + -4r)' equal to zero and attempt to solve: Simplifying 1 + -4r = 0 Solving 1 + -4r = 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 + -4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4r = 0 + -1 -4r = 0 + -1 Combine like terms: 0 + -1 = -1 -4r = -1 Divide each side by '-4'. r = 0.25 Simplifying r = 0.25Solution
r = {0, -2, 0.25}
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