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Simplifying 15r3 + 5r2 + -120r = 0 Reorder the terms: -120r + 5r2 + 15r3 = 0 Solving -120r + 5r2 + 15r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '5r'. 5r(-24 + r + 3r2) = 0 Factor a trinomial. 5r((-3 + -1r)(8 + -3r)) = 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 '(-3 + -1r)' equal to zero and attempt to solve: Simplifying -3 + -1r = 0 Solving -3 + -1r = 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 + -1r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1r = 0 + 3 -1r = 0 + 3 Combine like terms: 0 + 3 = 3 -1r = 3 Divide each side by '-1'. r = -3 Simplifying r = -3Subproblem 3
Set the factor '(8 + -3r)' equal to zero and attempt to solve: Simplifying 8 + -3r = 0 Solving 8 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3r = 0 + -8 -3r = 0 + -8 Combine like terms: 0 + -8 = -8 -3r = -8 Divide each side by '-3'. r = 2.666666667 Simplifying r = 2.666666667Solution
r = {0, -3, 2.666666667}
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