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Simplifying 32r5 + -60r4 + -27r3 = 0 Reorder the terms: -27r3 + -60r4 + 32r5 = 0 Solving -27r3 + -60r4 + 32r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), 'r3'. r3(-27 + -60r + 32r2) = 0 Factor a trinomial. r3((-3 + -8r)(9 + -4r)) = 0Subproblem 1
Set the factor 'r3' equal to zero and attempt to solve: Simplifying r3 = 0 Solving r3 = 0 Move all terms containing r to the left, all other terms to the right. Simplifying r3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3 + -8r)' equal to zero and attempt to solve: Simplifying -3 + -8r = 0 Solving -3 + -8r = 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 + -8r = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8r = 0 + 3 -8r = 0 + 3 Combine like terms: 0 + 3 = 3 -8r = 3 Divide each side by '-8'. r = -0.375 Simplifying r = -0.375Subproblem 3
Set the factor '(9 + -4r)' equal to zero and attempt to solve: Simplifying 9 + -4r = 0 Solving 9 + -4r = 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 + -4r = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4r = 0 + -9 -4r = 0 + -9 Combine like terms: 0 + -9 = -9 -4r = -9 Divide each side by '-4'. r = 2.25 Simplifying r = 2.25Solution
r = {-0.375, 2.25}
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