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Simplifying 64r3 = 4r Solving 64r3 = 4r Solving for variable 'r'. Reorder the terms: -4r + 64r3 = 4r + -4r Combine like terms: 4r + -4r = 0 -4r + 64r3 = 0 Factor out the Greatest Common Factor (GCF), '4r'. 4r(-1 + 16r2) = 0 Factor a difference between two squares. 4r((1 + 4r)(-1 + 4r)) = 0 Ignore the factor 4.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 '(1 + 4r)' equal to zero and attempt to solve: Simplifying 1 + 4r = 0 Solving 1 + 4r = 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 + 4r = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4r = 0 + -1 4r = 0 + -1 Combine like terms: 0 + -1 = -1 4r = -1 Divide each side by '4'. r = -0.25 Simplifying r = -0.25Subproblem 3
Set the factor '(-1 + 4r)' equal to zero and attempt to solve: Simplifying -1 + 4r = 0 Solving -1 + 4r = 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 + 4r = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4r = 0 + 1 4r = 0 + 1 Combine like terms: 0 + 1 = 1 4r = 1 Divide each side by '4'. r = 0.25 Simplifying r = 0.25Solution
r = {0, -0.25, 0.25}
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