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Simplifying 4r5 + -16r4 + 12r3 = 0 Reorder the terms: 12r3 + -16r4 + 4r5 = 0 Solving 12r3 + -16r4 + 4r5 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '4r3'. 4r3(3 + -4r + r2) = 0 Factor a trinomial. 4r3((1 + -1r)(3 + -1r)) = 0 Ignore the factor 4.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 '(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 = 1Subproblem 3
Set the factor '(3 + -1r)' equal to zero and attempt to solve: Simplifying 3 + -1r = 0 Solving 3 + -1r = 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 + -1r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1r = 0 + -3 -1r = 0 + -3 Combine like terms: 0 + -3 = -3 -1r = -3 Divide each side by '-1'. r = 3 Simplifying r = 3Solution
r = {1, 3}
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