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Simplifying -2r(1 + 4r) + 8r(-1r + 4) = 0 (1 * -2r + 4r * -2r) + 8r(-1r + 4) = 0 (-2r + -8r2) + 8r(-1r + 4) = 0 Reorder the terms: -2r + -8r2 + 8r(4 + -1r) = 0 -2r + -8r2 + (4 * 8r + -1r * 8r) = 0 -2r + -8r2 + (32r + -8r2) = 0 Reorder the terms: -2r + 32r + -8r2 + -8r2 = 0 Combine like terms: -2r + 32r = 30r 30r + -8r2 + -8r2 = 0 Combine like terms: -8r2 + -8r2 = -16r2 30r + -16r2 = 0 Solving 30r + -16r2 = 0 Solving for variable 'r'. Factor out the Greatest Common Factor (GCF), '2r'. 2r(15 + -8r) = 0 Ignore the factor 2.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 '(15 + -8r)' equal to zero and attempt to solve: Simplifying 15 + -8r = 0 Solving 15 + -8r = 0 Move all terms containing r to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -8r = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -8r = 0 + -15 -8r = 0 + -15 Combine like terms: 0 + -15 = -15 -8r = -15 Divide each side by '-8'. r = 1.875 Simplifying r = 1.875Solution
r = {0, 1.875}
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