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Simplifying (8r + -4)(r + 5) + -1(3r + -1)(r + 5) = 0 Reorder the terms: (-4 + 8r)(r + 5) + -1(3r + -1)(r + 5) = 0 Reorder the terms: (-4 + 8r)(5 + r) + -1(3r + -1)(r + 5) = 0 Multiply (-4 + 8r) * (5 + r) (-4(5 + r) + 8r * (5 + r)) + -1(3r + -1)(r + 5) = 0 ((5 * -4 + r * -4) + 8r * (5 + r)) + -1(3r + -1)(r + 5) = 0 ((-20 + -4r) + 8r * (5 + r)) + -1(3r + -1)(r + 5) = 0 (-20 + -4r + (5 * 8r + r * 8r)) + -1(3r + -1)(r + 5) = 0 (-20 + -4r + (40r + 8r2)) + -1(3r + -1)(r + 5) = 0 Combine like terms: -4r + 40r = 36r (-20 + 36r + 8r2) + -1(3r + -1)(r + 5) = 0 Reorder the terms: -20 + 36r + 8r2 + -1(-1 + 3r)(r + 5) = 0 Reorder the terms: -20 + 36r + 8r2 + -1(-1 + 3r)(5 + r) = 0 Multiply (-1 + 3r) * (5 + r) -20 + 36r + 8r2 + -1(-1(5 + r) + 3r * (5 + r)) = 0 -20 + 36r + 8r2 + -1((5 * -1 + r * -1) + 3r * (5 + r)) = 0 -20 + 36r + 8r2 + -1((-5 + -1r) + 3r * (5 + r)) = 0 -20 + 36r + 8r2 + -1(-5 + -1r + (5 * 3r + r * 3r)) = 0 -20 + 36r + 8r2 + -1(-5 + -1r + (15r + 3r2)) = 0 Combine like terms: -1r + 15r = 14r -20 + 36r + 8r2 + -1(-5 + 14r + 3r2) = 0 -20 + 36r + 8r2 + (-5 * -1 + 14r * -1 + 3r2 * -1) = 0 -20 + 36r + 8r2 + (5 + -14r + -3r2) = 0 Reorder the terms: -20 + 5 + 36r + -14r + 8r2 + -3r2 = 0 Combine like terms: -20 + 5 = -15 -15 + 36r + -14r + 8r2 + -3r2 = 0 Combine like terms: 36r + -14r = 22r -15 + 22r + 8r2 + -3r2 = 0 Combine like terms: 8r2 + -3r2 = 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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