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Simplifying 3r2(r + -4) = 135r Reorder the terms: 3r2(-4 + r) = 135r (-4 * 3r2 + r * 3r2) = 135r (-12r2 + 3r3) = 135r Solving -12r2 + 3r3 = 135r Solving for variable 'r'. Reorder the terms: -135r + -12r2 + 3r3 = 135r + -135r Combine like terms: 135r + -135r = 0 -135r + -12r2 + 3r3 = 0 Factor out the Greatest Common Factor (GCF), '3r'. 3r(-45 + -4r + r2) = 0 Factor a trinomial. 3r((-5 + -1r)(9 + -1r)) = 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 '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 3
Set the factor '(9 + -1r)' equal to zero and attempt to solve: Simplifying 9 + -1r = 0 Solving 9 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1r = 0 + -9 -1r = 0 + -9 Combine like terms: 0 + -9 = -9 -1r = -9 Divide each side by '-1'. r = 9 Simplifying r = 9Solution
r = {0, -5, 9}
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