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Simplifying 3r3 + 27r2 + 24r = 0 Reorder the terms: 24r + 27r2 + 3r3 = 0 Solving 24r + 27r2 + 3r3 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r'. 3r(8 + 9r + r2) = 0 Factor a trinomial. 3r((8 + r)(1 + r)) = 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 '(8 + r)' equal to zero and attempt to solve: Simplifying 8 + r = 0 Solving 8 + r = 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 + r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + r = 0 + -8 r = 0 + -8 Combine like terms: 0 + -8 = -8 r = -8 Simplifying r = -8Subproblem 3
Set the factor '(1 + r)' equal to zero and attempt to solve: Simplifying 1 + r = 0 Solving 1 + r = 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 + r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + r = 0 + -1 r = 0 + -1 Combine like terms: 0 + -1 = -1 r = -1 Simplifying r = -1Solution
r = {0, -8, -1}
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