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Simplifying r2 + -3r = 2r + 14 Reorder the terms: -3r + r2 = 2r + 14 Reorder the terms: -3r + r2 = 14 + 2r Solving -3r + r2 = 14 + 2r Solving for variable 'r'. Reorder the terms: -14 + -3r + -2r + r2 = 14 + 2r + -14 + -2r Combine like terms: -3r + -2r = -5r -14 + -5r + r2 = 14 + 2r + -14 + -2r Reorder the terms: -14 + -5r + r2 = 14 + -14 + 2r + -2r Combine like terms: 14 + -14 = 0 -14 + -5r + r2 = 0 + 2r + -2r -14 + -5r + r2 = 2r + -2r Combine like terms: 2r + -2r = 0 -14 + -5r + r2 = 0 Factor a trinomial. (-2 + -1r)(7 + -1r) = 0Subproblem 1
Set the factor '(-2 + -1r)' equal to zero and attempt to solve: Simplifying -2 + -1r = 0 Solving -2 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1r = 0 + 2 -1r = 0 + 2 Combine like terms: 0 + 2 = 2 -1r = 2 Divide each side by '-1'. r = -2 Simplifying r = -2Subproblem 2
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 = 7Solution
r = {-2, 7}
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