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Simplifying (7r + -4)(r + 5) + -1(2r + -1)(r + 5) = 0 Reorder the terms: (-4 + 7r)(r + 5) + -1(2r + -1)(r + 5) = 0 Reorder the terms: (-4 + 7r)(5 + r) + -1(2r + -1)(r + 5) = 0 Multiply (-4 + 7r) * (5 + r) (-4(5 + r) + 7r * (5 + r)) + -1(2r + -1)(r + 5) = 0 ((5 * -4 + r * -4) + 7r * (5 + r)) + -1(2r + -1)(r + 5) = 0 ((-20 + -4r) + 7r * (5 + r)) + -1(2r + -1)(r + 5) = 0 (-20 + -4r + (5 * 7r + r * 7r)) + -1(2r + -1)(r + 5) = 0 (-20 + -4r + (35r + 7r2)) + -1(2r + -1)(r + 5) = 0 Combine like terms: -4r + 35r = 31r (-20 + 31r + 7r2) + -1(2r + -1)(r + 5) = 0 Reorder the terms: -20 + 31r + 7r2 + -1(-1 + 2r)(r + 5) = 0 Reorder the terms: -20 + 31r + 7r2 + -1(-1 + 2r)(5 + r) = 0 Multiply (-1 + 2r) * (5 + r) -20 + 31r + 7r2 + -1(-1(5 + r) + 2r * (5 + r)) = 0 -20 + 31r + 7r2 + -1((5 * -1 + r * -1) + 2r * (5 + r)) = 0 -20 + 31r + 7r2 + -1((-5 + -1r) + 2r * (5 + r)) = 0 -20 + 31r + 7r2 + -1(-5 + -1r + (5 * 2r + r * 2r)) = 0 -20 + 31r + 7r2 + -1(-5 + -1r + (10r + 2r2)) = 0 Combine like terms: -1r + 10r = 9r -20 + 31r + 7r2 + -1(-5 + 9r + 2r2) = 0 -20 + 31r + 7r2 + (-5 * -1 + 9r * -1 + 2r2 * -1) = 0 -20 + 31r + 7r2 + (5 + -9r + -2r2) = 0 Reorder the terms: -20 + 5 + 31r + -9r + 7r2 + -2r2 = 0 Combine like terms: -20 + 5 = -15 -15 + 31r + -9r + 7r2 + -2r2 = 0 Combine like terms: 31r + -9r = 22r -15 + 22r + 7r2 + -2r2 = 0 Combine like terms: 7r2 + -2r2 = 5r2 -15 + 22r + 5r2 = 0 Solving -15 + 22r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -1r)(3 + -5r) = 0Subproblem 1
Set the factor '(-5 + -1r)' equal to zero and attempt to solve: Simplifying -5 + -1r = 0 Solving -5 + -1r = 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 + -1r = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1r = 0 + 5 -1r = 0 + 5 Combine like terms: 0 + 5 = 5 -1r = 5 Divide each side by '-1'. r = -5 Simplifying r = -5Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve: Simplifying 3 + -5r = 0 Solving 3 + -5r = 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 + -5r = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5r = 0 + -3 -5r = 0 + -3 Combine like terms: 0 + -3 = -3 -5r = -3 Divide each side by '-5'. r = 0.6 Simplifying r = 0.6Solution
r = {-5, 0.6}
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