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Simplifying 12r2 = -68r + 112 Reorder the terms: 12r2 = 112 + -68r Solving 12r2 = 112 + -68r Solving for variable 'r'. Reorder the terms: -112 + 68r + 12r2 = 112 + -68r + -112 + 68r Reorder the terms: -112 + 68r + 12r2 = 112 + -112 + -68r + 68r Combine like terms: 112 + -112 = 0 -112 + 68r + 12r2 = 0 + -68r + 68r -112 + 68r + 12r2 = -68r + 68r Combine like terms: -68r + 68r = 0 -112 + 68r + 12r2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-28 + 17r + 3r2) = 0 Factor a trinomial. 4((-7 + -1r)(4 + -3r)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve: Simplifying -7 + -1r = 0 Solving -7 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1r = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1r = 0 + 7 -1r = 0 + 7 Combine like terms: 0 + 7 = 7 -1r = 7 Divide each side by '-1'. r = -7 Simplifying r = -7Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {-7, 1.333333333}
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