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Simplifying -20 + 2r2 = 3r2 + 9r Reorder the terms: -20 + 2r2 = 9r + 3r2 Solving -20 + 2r2 = 9r + 3r2 Solving for variable 'r'. Reorder the terms: -20 + -9r + 2r2 + -3r2 = 9r + 3r2 + -9r + -3r2 Combine like terms: 2r2 + -3r2 = -1r2 -20 + -9r + -1r2 = 9r + 3r2 + -9r + -3r2 Reorder the terms: -20 + -9r + -1r2 = 9r + -9r + 3r2 + -3r2 Combine like terms: 9r + -9r = 0 -20 + -9r + -1r2 = 0 + 3r2 + -3r2 -20 + -9r + -1r2 = 3r2 + -3r2 Combine like terms: 3r2 + -3r2 = 0 -20 + -9r + -1r2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 9r + r2) = 0 Factor a trinomial. -1((5 + r)(4 + r)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + r)' equal to zero and attempt to solve: Simplifying 5 + r = 0 Solving 5 + r = 0 Move all terms containing r to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + r = 0 + -5 r = 0 + -5 Combine like terms: 0 + -5 = -5 r = -5 Simplifying r = -5Subproblem 2
Set the factor '(4 + r)' equal to zero and attempt to solve: Simplifying 4 + r = 0 Solving 4 + r = 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 + r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + r = 0 + -4 r = 0 + -4 Combine like terms: 0 + -4 = -4 r = -4 Simplifying r = -4Solution
r = {-5, -4}
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