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Simplifying (7r + -5)(r + 6) + -1(4r + -1)(r + 6) = 0 Reorder the terms: (-5 + 7r)(r + 6) + -1(4r + -1)(r + 6) = 0 Reorder the terms: (-5 + 7r)(6 + r) + -1(4r + -1)(r + 6) = 0 Multiply (-5 + 7r) * (6 + r) (-5(6 + r) + 7r * (6 + r)) + -1(4r + -1)(r + 6) = 0 ((6 * -5 + r * -5) + 7r * (6 + r)) + -1(4r + -1)(r + 6) = 0 ((-30 + -5r) + 7r * (6 + r)) + -1(4r + -1)(r + 6) = 0 (-30 + -5r + (6 * 7r + r * 7r)) + -1(4r + -1)(r + 6) = 0 (-30 + -5r + (42r + 7r2)) + -1(4r + -1)(r + 6) = 0 Combine like terms: -5r + 42r = 37r (-30 + 37r + 7r2) + -1(4r + -1)(r + 6) = 0 Reorder the terms: -30 + 37r + 7r2 + -1(-1 + 4r)(r + 6) = 0 Reorder the terms: -30 + 37r + 7r2 + -1(-1 + 4r)(6 + r) = 0 Multiply (-1 + 4r) * (6 + r) -30 + 37r + 7r2 + -1(-1(6 + r) + 4r * (6 + r)) = 0 -30 + 37r + 7r2 + -1((6 * -1 + r * -1) + 4r * (6 + r)) = 0 -30 + 37r + 7r2 + -1((-6 + -1r) + 4r * (6 + r)) = 0 -30 + 37r + 7r2 + -1(-6 + -1r + (6 * 4r + r * 4r)) = 0 -30 + 37r + 7r2 + -1(-6 + -1r + (24r + 4r2)) = 0 Combine like terms: -1r + 24r = 23r -30 + 37r + 7r2 + -1(-6 + 23r + 4r2) = 0 -30 + 37r + 7r2 + (-6 * -1 + 23r * -1 + 4r2 * -1) = 0 -30 + 37r + 7r2 + (6 + -23r + -4r2) = 0 Reorder the terms: -30 + 6 + 37r + -23r + 7r2 + -4r2 = 0 Combine like terms: -30 + 6 = -24 -24 + 37r + -23r + 7r2 + -4r2 = 0 Combine like terms: 37r + -23r = 14r -24 + 14r + 7r2 + -4r2 = 0 Combine like terms: 7r2 + -4r2 = 3r2 -24 + 14r + 3r2 = 0 Solving -24 + 14r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-6 + -1r)(4 + -3r) = 0Subproblem 1
Set the factor '(-6 + -1r)' equal to zero and attempt to solve: Simplifying -6 + -1r = 0 Solving -6 + -1r = 0 Move all terms containing r to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1r = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1r = 0 + 6 -1r = 0 + 6 Combine like terms: 0 + 6 = 6 -1r = 6 Divide each side by '-1'. r = -6 Simplifying r = -6Subproblem 2
Set the factor '(4 + -3r)' equal to zero and attempt to solve: Simplifying 4 + -3r = 0 Solving 4 + -3r = 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 + -3r = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3r = 0 + -4 -3r = 0 + -4 Combine like terms: 0 + -4 = -4 -3r = -4 Divide each side by '-3'. r = 1.333333333 Simplifying r = 1.333333333Solution
r = {-6, 1.333333333}
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