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Simplifying (3r + -2)(r + -6) = -13r + 18 Reorder the terms: (-2 + 3r)(r + -6) = -13r + 18 Reorder the terms: (-2 + 3r)(-6 + r) = -13r + 18 Multiply (-2 + 3r) * (-6 + r) (-2(-6 + r) + 3r * (-6 + r)) = -13r + 18 ((-6 * -2 + r * -2) + 3r * (-6 + r)) = -13r + 18 ((12 + -2r) + 3r * (-6 + r)) = -13r + 18 (12 + -2r + (-6 * 3r + r * 3r)) = -13r + 18 (12 + -2r + (-18r + 3r2)) = -13r + 18 Combine like terms: -2r + -18r = -20r (12 + -20r + 3r2) = -13r + 18 Reorder the terms: 12 + -20r + 3r2 = 18 + -13r Solving 12 + -20r + 3r2 = 18 + -13r Solving for variable 'r'. Reorder the terms: 12 + -18 + -20r + 13r + 3r2 = 18 + -13r + -18 + 13r Combine like terms: 12 + -18 = -6 -6 + -20r + 13r + 3r2 = 18 + -13r + -18 + 13r Combine like terms: -20r + 13r = -7r -6 + -7r + 3r2 = 18 + -13r + -18 + 13r Reorder the terms: -6 + -7r + 3r2 = 18 + -18 + -13r + 13r Combine like terms: 18 + -18 = 0 -6 + -7r + 3r2 = 0 + -13r + 13r -6 + -7r + 3r2 = -13r + 13r Combine like terms: -13r + 13r = 0 -6 + -7r + 3r2 = 0 Factor a trinomial. (-2 + -3r)(3 + -1r) = 0Subproblem 1
Set the factor '(-2 + -3r)' equal to zero and attempt to solve: Simplifying -2 + -3r = 0 Solving -2 + -3r = 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 + -3r = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3r = 0 + 2 -3r = 0 + 2 Combine like terms: 0 + 2 = 2 -3r = 2 Divide each side by '-3'. r = -0.6666666667 Simplifying r = -0.6666666667Subproblem 2
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 = 3Solution
r = {-0.6666666667, 3}
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