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Simplifying 8r3 + 24r2 = 32r Reorder the terms: 24r2 + 8r3 = 32r Solving 24r2 + 8r3 = 32r Solving for variable 'r'. Reorder the terms: -32r + 24r2 + 8r3 = 32r + -32r Combine like terms: 32r + -32r = 0 -32r + 24r2 + 8r3 = 0 Factor out the Greatest Common Factor (GCF), '8r'. 8r(-4 + 3r + r2) = 0 Factor a trinomial. 8r((-4 + -1r)(1 + -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 '(-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 + -1r)' equal to zero and attempt to solve: Simplifying 1 + -1r = 0 Solving 1 + -1r = 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 + -1r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1r = 0 + -1 -1r = 0 + -1 Combine like terms: 0 + -1 = -1 -1r = -1 Divide each side by '-1'. r = 1 Simplifying r = 1Solution
r = {0, -4, 1}
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