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Simplifying r5 + 10r4 = 24r3 Reorder the terms: 10r4 + r5 = 24r3 Solving 10r4 + r5 = 24r3 Solving for variable 'r'. Reorder the terms: -24r3 + 10r4 + r5 = 24r3 + -24r3 Combine like terms: 24r3 + -24r3 = 0 -24r3 + 10r4 + r5 = 0 Factor out the Greatest Common Factor (GCF), 'r3'. r3(-24 + 10r + r2) = 0 Factor a trinomial. r3((-12 + -1r)(2 + -1r)) = 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 '(-12 + -1r)' equal to zero and attempt to solve: Simplifying -12 + -1r = 0 Solving -12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1r = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1r = 0 + 12 -1r = 0 + 12 Combine like terms: 0 + 12 = 12 -1r = 12 Divide each side by '-1'. r = -12 Simplifying r = -12Subproblem 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 = {-12, 2}
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