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Simplifying 3r2 + -9r + -17 = 2r2 + -5 + -8r Reorder the terms: -17 + -9r + 3r2 = 2r2 + -5 + -8r Reorder the terms: -17 + -9r + 3r2 = -5 + -8r + 2r2 Solving -17 + -9r + 3r2 = -5 + -8r + 2r2 Solving for variable 'r'. Reorder the terms: -17 + 5 + -9r + 8r + 3r2 + -2r2 = -5 + -8r + 2r2 + 5 + 8r + -2r2 Combine like terms: -17 + 5 = -12 -12 + -9r + 8r + 3r2 + -2r2 = -5 + -8r + 2r2 + 5 + 8r + -2r2 Combine like terms: -9r + 8r = -1r -12 + -1r + 3r2 + -2r2 = -5 + -8r + 2r2 + 5 + 8r + -2r2 Combine like terms: 3r2 + -2r2 = 1r2 -12 + -1r + 1r2 = -5 + -8r + 2r2 + 5 + 8r + -2r2 Reorder the terms: -12 + -1r + 1r2 = -5 + 5 + -8r + 8r + 2r2 + -2r2 Combine like terms: -5 + 5 = 0 -12 + -1r + 1r2 = 0 + -8r + 8r + 2r2 + -2r2 -12 + -1r + 1r2 = -8r + 8r + 2r2 + -2r2 Combine like terms: -8r + 8r = 0 -12 + -1r + 1r2 = 0 + 2r2 + -2r2 -12 + -1r + 1r2 = 2r2 + -2r2 Combine like terms: 2r2 + -2r2 = 0 -12 + -1r + 1r2 = 0 Factor a trinomial. (-3 + -1r)(4 + -1r) = 0Subproblem 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 '(4 + -1r)' equal to zero and attempt to solve: Simplifying 4 + -1r = 0 Solving 4 + -1r = 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 + -1r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1r = 0 + -4 -1r = 0 + -4 Combine like terms: 0 + -4 = -4 -1r = -4 Divide each side by '-1'. r = 4 Simplifying r = 4Solution
r = {-3, 4}
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