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Simplifying 48r5 + -243r3 = 0 Reorder the terms: -243r3 + 48r5 = 0 Solving -243r3 + 48r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '3r3'. 3r3(-81 + 16r2) = 0 Factor a difference between two squares. 3r3((9 + 4r)(-9 + 4r)) = 0 Ignore the factor 3.Subproblem 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 '(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 = -2.25Subproblem 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 = {-2.25, 2.25}
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