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Simplifying 2r2 = 9 + -3r Solving 2r2 = 9 + -3r Solving for variable 'r'. Reorder the terms: -9 + 3r + 2r2 = 9 + -3r + -9 + 3r Reorder the terms: -9 + 3r + 2r2 = 9 + -9 + -3r + 3r Combine like terms: 9 + -9 = 0 -9 + 3r + 2r2 = 0 + -3r + 3r -9 + 3r + 2r2 = -3r + 3r Combine like terms: -3r + 3r = 0 -9 + 3r + 2r2 = 0 Factor a trinomial. (-3 + -1r)(3 + -2r) = 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 '(3 + -2r)' equal to zero and attempt to solve: Simplifying 3 + -2r = 0 Solving 3 + -2r = 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 + -2r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2r = 0 + -3 -2r = 0 + -3 Combine like terms: 0 + -3 = -3 -2r = -3 Divide each side by '-2'. r = 1.5 Simplifying r = 1.5Solution
r = {-3, 1.5}
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