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Simplifying 2r2 = 8r + 192 Reorder the terms: 2r2 = 192 + 8r Solving 2r2 = 192 + 8r Solving for variable 'r'. Reorder the terms: -192 + -8r + 2r2 = 192 + 8r + -192 + -8r Reorder the terms: -192 + -8r + 2r2 = 192 + -192 + 8r + -8r Combine like terms: 192 + -192 = 0 -192 + -8r + 2r2 = 0 + 8r + -8r -192 + -8r + 2r2 = 8r + -8r Combine like terms: 8r + -8r = 0 -192 + -8r + 2r2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + -4r + r2) = 0 Factor a trinomial. 2((-8 + -1r)(12 + -1r)) = 0 Ignore the factor 2.Subproblem 1
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 = -8Subproblem 2
Set the factor '(12 + -1r)' equal to zero and attempt to solve: Simplifying 12 + -1r = 0 Solving 12 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1r = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1r = 0 + -12 -1r = 0 + -12 Combine like terms: 0 + -12 = -12 -1r = -12 Divide each side by '-1'. r = 12 Simplifying r = 12Solution
r = {-8, 12}
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