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Simplifying 10r3 + 38r2 + -8r = 0 Reorder the terms: -8r + 38r2 + 10r3 = 0 Solving -8r + 38r2 + 10r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(-4 + 19r + 5r2) = 0 Factor a trinomial. 2r((-4 + -1r)(1 + -5r)) = 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 '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 3
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 = 0.2Solution
r = {0, -4, 0.2}
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