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Simplifying (7r + -8)(r + 4) + -1(4r + -1)(r + 4) = 0 Reorder the terms: (-8 + 7r)(r + 4) + -1(4r + -1)(r + 4) = 0 Reorder the terms: (-8 + 7r)(4 + r) + -1(4r + -1)(r + 4) = 0 Multiply (-8 + 7r) * (4 + r) (-8(4 + r) + 7r * (4 + r)) + -1(4r + -1)(r + 4) = 0 ((4 * -8 + r * -8) + 7r * (4 + r)) + -1(4r + -1)(r + 4) = 0 ((-32 + -8r) + 7r * (4 + r)) + -1(4r + -1)(r + 4) = 0 (-32 + -8r + (4 * 7r + r * 7r)) + -1(4r + -1)(r + 4) = 0 (-32 + -8r + (28r + 7r2)) + -1(4r + -1)(r + 4) = 0 Combine like terms: -8r + 28r = 20r (-32 + 20r + 7r2) + -1(4r + -1)(r + 4) = 0 Reorder the terms: -32 + 20r + 7r2 + -1(-1 + 4r)(r + 4) = 0 Reorder the terms: -32 + 20r + 7r2 + -1(-1 + 4r)(4 + r) = 0 Multiply (-1 + 4r) * (4 + r) -32 + 20r + 7r2 + -1(-1(4 + r) + 4r * (4 + r)) = 0 -32 + 20r + 7r2 + -1((4 * -1 + r * -1) + 4r * (4 + r)) = 0 -32 + 20r + 7r2 + -1((-4 + -1r) + 4r * (4 + r)) = 0 -32 + 20r + 7r2 + -1(-4 + -1r + (4 * 4r + r * 4r)) = 0 -32 + 20r + 7r2 + -1(-4 + -1r + (16r + 4r2)) = 0 Combine like terms: -1r + 16r = 15r -32 + 20r + 7r2 + -1(-4 + 15r + 4r2) = 0 -32 + 20r + 7r2 + (-4 * -1 + 15r * -1 + 4r2 * -1) = 0 -32 + 20r + 7r2 + (4 + -15r + -4r2) = 0 Reorder the terms: -32 + 4 + 20r + -15r + 7r2 + -4r2 = 0 Combine like terms: -32 + 4 = -28 -28 + 20r + -15r + 7r2 + -4r2 = 0 Combine like terms: 20r + -15r = 5r -28 + 5r + 7r2 + -4r2 = 0 Combine like terms: 7r2 + -4r2 = 3r2 -28 + 5r + 3r2 = 0 Solving -28 + 5r + 3r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -1r)(7 + -3r) = 0Subproblem 1
Set the factor '(-4 + -1r)' equal to zero and attempt to solve: Simplifying -4 + -1r = 0 Solving -4 + -1r = 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 + -1r = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1r = 0 + 4 -1r = 0 + 4 Combine like terms: 0 + 4 = 4 -1r = 4 Divide each side by '-1'. r = -4 Simplifying r = -4Subproblem 2
Set the factor '(7 + -3r)' equal to zero and attempt to solve: Simplifying 7 + -3r = 0 Solving 7 + -3r = 0 Move all terms containing r to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -3r = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3r = 0 + -7 -3r = 0 + -7 Combine like terms: 0 + -7 = -7 -3r = -7 Divide each side by '-3'. r = 2.333333333 Simplifying r = 2.333333333Solution
r = {-4, 2.333333333}
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