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Simplifying 4r2 = 20r + 96 Reorder the terms: 4r2 = 96 + 20r Solving 4r2 = 96 + 20r Solving for variable 'r'. Reorder the terms: -96 + -20r + 4r2 = 96 + 20r + -96 + -20r Reorder the terms: -96 + -20r + 4r2 = 96 + -96 + 20r + -20r Combine like terms: 96 + -96 = 0 -96 + -20r + 4r2 = 0 + 20r + -20r -96 + -20r + 4r2 = 20r + -20r Combine like terms: 20r + -20r = 0 -96 + -20r + 4r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + -5r + r2) = 0 Factor a trinomial. 4((-3 + -1r)(8 + -1r)) = 0 Ignore the factor 4.Subproblem 1
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 = -3Subproblem 2
Set the factor '(8 + -1r)' equal to zero and attempt to solve: Simplifying 8 + -1r = 0 Solving 8 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1r = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1r = 0 + -8 -1r = 0 + -8 Combine like terms: 0 + -8 = -8 -1r = -8 Divide each side by '-1'. r = 8 Simplifying r = 8Solution
r = {-3, 8}
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