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Simplifying (7r + -5)(r + 5) + -1(4r + -1)(r + 5) = 0 Reorder the terms: (-5 + 7r)(r + 5) + -1(4r + -1)(r + 5) = 0 Reorder the terms: (-5 + 7r)(5 + r) + -1(4r + -1)(r + 5) = 0 Multiply (-5 + 7r) * (5 + r) (-5(5 + r) + 7r * (5 + r)) + -1(4r + -1)(r + 5) = 0 ((5 * -5 + r * -5) + 7r * (5 + r)) + -1(4r + -1)(r + 5) = 0 ((-25 + -5r) + 7r * (5 + r)) + -1(4r + -1)(r + 5) = 0 (-25 + -5r + (5 * 7r + r * 7r)) + -1(4r + -1)(r + 5) = 0 (-25 + -5r + (35r + 7r2)) + -1(4r + -1)(r + 5) = 0 Combine like terms: -5r + 35r = 30r (-25 + 30r + 7r2) + -1(4r + -1)(r + 5) = 0 Reorder the terms: -25 + 30r + 7r2 + -1(-1 + 4r)(r + 5) = 0 Reorder the terms: -25 + 30r + 7r2 + -1(-1 + 4r)(5 + r) = 0 Multiply (-1 + 4r) * (5 + r) -25 + 30r + 7r2 + -1(-1(5 + r) + 4r * (5 + r)) = 0 -25 + 30r + 7r2 + -1((5 * -1 + r * -1) + 4r * (5 + r)) = 0 -25 + 30r + 7r2 + -1((-5 + -1r) + 4r * (5 + r)) = 0 -25 + 30r + 7r2 + -1(-5 + -1r + (5 * 4r + r * 4r)) = 0 -25 + 30r + 7r2 + -1(-5 + -1r + (20r + 4r2)) = 0 Combine like terms: -1r + 20r = 19r -25 + 30r + 7r2 + -1(-5 + 19r + 4r2) = 0 -25 + 30r + 7r2 + (-5 * -1 + 19r * -1 + 4r2 * -1) = 0 -25 + 30r + 7r2 + (5 + -19r + -4r2) = 0 Reorder the terms: -25 + 5 + 30r + -19r + 7r2 + -4r2 = 0 Combine like terms: -25 + 5 = -20 -20 + 30r + -19r + 7r2 + -4r2 = 0 Combine like terms: 30r + -19r = 11r -20 + 11r + 7r2 + -4r2 = 0 Combine like terms: 7r2 + -4r2 = 3r2 -20 + 11r + 3r2 = 0 Solving -20 + 11r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-5 + -1r)(4 + -3r) = 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 '(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 = {-5, 1.333333333}
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