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Simplifying 9r2 + 80r = r2 + -168 Reorder the terms: 80r + 9r2 = r2 + -168 Reorder the terms: 80r + 9r2 = -168 + r2 Solving 80r + 9r2 = -168 + r2 Solving for variable 'r'. Reorder the terms: 168 + 80r + 9r2 + -1r2 = -168 + r2 + 168 + -1r2 Combine like terms: 9r2 + -1r2 = 8r2 168 + 80r + 8r2 = -168 + r2 + 168 + -1r2 Reorder the terms: 168 + 80r + 8r2 = -168 + 168 + r2 + -1r2 Combine like terms: -168 + 168 = 0 168 + 80r + 8r2 = 0 + r2 + -1r2 168 + 80r + 8r2 = r2 + -1r2 Combine like terms: r2 + -1r2 = 0 168 + 80r + 8r2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(21 + 10r + r2) = 0 Factor a trinomial. 8((7 + r)(3 + r)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + r)' equal to zero and attempt to solve: Simplifying 7 + r = 0 Solving 7 + r = 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 + r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + r = 0 + -7 r = 0 + -7 Combine like terms: 0 + -7 = -7 r = -7 Simplifying r = -7Subproblem 2
Set the factor '(3 + r)' equal to zero and attempt to solve: Simplifying 3 + r = 0 Solving 3 + r = 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 + r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + r = 0 + -3 r = 0 + -3 Combine like terms: 0 + -3 = -3 r = -3 Simplifying r = -3Solution
r = {-7, -3}
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