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Simplifying (5r + -6)(r + 3) + -1(2r + -1)(r + 3) = 0 Reorder the terms: (-6 + 5r)(r + 3) + -1(2r + -1)(r + 3) = 0 Reorder the terms: (-6 + 5r)(3 + r) + -1(2r + -1)(r + 3) = 0 Multiply (-6 + 5r) * (3 + r) (-6(3 + r) + 5r * (3 + r)) + -1(2r + -1)(r + 3) = 0 ((3 * -6 + r * -6) + 5r * (3 + r)) + -1(2r + -1)(r + 3) = 0 ((-18 + -6r) + 5r * (3 + r)) + -1(2r + -1)(r + 3) = 0 (-18 + -6r + (3 * 5r + r * 5r)) + -1(2r + -1)(r + 3) = 0 (-18 + -6r + (15r + 5r2)) + -1(2r + -1)(r + 3) = 0 Combine like terms: -6r + 15r = 9r (-18 + 9r + 5r2) + -1(2r + -1)(r + 3) = 0 Reorder the terms: -18 + 9r + 5r2 + -1(-1 + 2r)(r + 3) = 0 Reorder the terms: -18 + 9r + 5r2 + -1(-1 + 2r)(3 + r) = 0 Multiply (-1 + 2r) * (3 + r) -18 + 9r + 5r2 + -1(-1(3 + r) + 2r * (3 + r)) = 0 -18 + 9r + 5r2 + -1((3 * -1 + r * -1) + 2r * (3 + r)) = 0 -18 + 9r + 5r2 + -1((-3 + -1r) + 2r * (3 + r)) = 0 -18 + 9r + 5r2 + -1(-3 + -1r + (3 * 2r + r * 2r)) = 0 -18 + 9r + 5r2 + -1(-3 + -1r + (6r + 2r2)) = 0 Combine like terms: -1r + 6r = 5r -18 + 9r + 5r2 + -1(-3 + 5r + 2r2) = 0 -18 + 9r + 5r2 + (-3 * -1 + 5r * -1 + 2r2 * -1) = 0 -18 + 9r + 5r2 + (3 + -5r + -2r2) = 0 Reorder the terms: -18 + 3 + 9r + -5r + 5r2 + -2r2 = 0 Combine like terms: -18 + 3 = -15 -15 + 9r + -5r + 5r2 + -2r2 = 0 Combine like terms: 9r + -5r = 4r -15 + 4r + 5r2 + -2r2 = 0 Combine like terms: 5r2 + -2r2 = 3r2 -15 + 4r + 3r2 = 0 Solving -15 + 4r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-3 + -1r)(5 + -3r) = 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 '(5 + -3r)' equal to zero and attempt to solve: Simplifying 5 + -3r = 0 Solving 5 + -3r = 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 + -3r = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3r = 0 + -5 -3r = 0 + -5 Combine like terms: 0 + -5 = -5 -3r = -5 Divide each side by '-3'. r = 1.666666667 Simplifying r = 1.666666667Solution
r = {-3, 1.666666667}
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