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Simplifying 8r3 + 32r2 = 96r Reorder the terms: 32r2 + 8r3 = 96r Solving 32r2 + 8r3 = 96r Solving for variable 'r'. Reorder the terms: -96r + 32r2 + 8r3 = 96r + -96r Combine like terms: 96r + -96r = 0 -96r + 32r2 + 8r3 = 0 Factor out the Greatest Common Factor (GCF), '8r'. 8r(-12 + 4r + r2) = 0 Factor a trinomial. 8r((-6 + -1r)(2 + -1r)) = 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 '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6Subproblem 3
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 = 2Solution
r = {0, -6, 2}
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