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Simplifying (8r + -4)(r + 4) + -1(3r + -1)(r + 4) = 0 Reorder the terms: (-4 + 8r)(r + 4) + -1(3r + -1)(r + 4) = 0 Reorder the terms: (-4 + 8r)(4 + r) + -1(3r + -1)(r + 4) = 0 Multiply (-4 + 8r) * (4 + r) (-4(4 + r) + 8r * (4 + r)) + -1(3r + -1)(r + 4) = 0 ((4 * -4 + r * -4) + 8r * (4 + r)) + -1(3r + -1)(r + 4) = 0 ((-16 + -4r) + 8r * (4 + r)) + -1(3r + -1)(r + 4) = 0 (-16 + -4r + (4 * 8r + r * 8r)) + -1(3r + -1)(r + 4) = 0 (-16 + -4r + (32r + 8r2)) + -1(3r + -1)(r + 4) = 0 Combine like terms: -4r + 32r = 28r (-16 + 28r + 8r2) + -1(3r + -1)(r + 4) = 0 Reorder the terms: -16 + 28r + 8r2 + -1(-1 + 3r)(r + 4) = 0 Reorder the terms: -16 + 28r + 8r2 + -1(-1 + 3r)(4 + r) = 0 Multiply (-1 + 3r) * (4 + r) -16 + 28r + 8r2 + -1(-1(4 + r) + 3r * (4 + r)) = 0 -16 + 28r + 8r2 + -1((4 * -1 + r * -1) + 3r * (4 + r)) = 0 -16 + 28r + 8r2 + -1((-4 + -1r) + 3r * (4 + r)) = 0 -16 + 28r + 8r2 + -1(-4 + -1r + (4 * 3r + r * 3r)) = 0 -16 + 28r + 8r2 + -1(-4 + -1r + (12r + 3r2)) = 0 Combine like terms: -1r + 12r = 11r -16 + 28r + 8r2 + -1(-4 + 11r + 3r2) = 0 -16 + 28r + 8r2 + (-4 * -1 + 11r * -1 + 3r2 * -1) = 0 -16 + 28r + 8r2 + (4 + -11r + -3r2) = 0 Reorder the terms: -16 + 4 + 28r + -11r + 8r2 + -3r2 = 0 Combine like terms: -16 + 4 = -12 -12 + 28r + -11r + 8r2 + -3r2 = 0 Combine like terms: 28r + -11r = 17r -12 + 17r + 8r2 + -3r2 = 0 Combine like terms: 8r2 + -3r2 = 5r2 -12 + 17r + 5r2 = 0 Solving -12 + 17r + 5r2 = 0 Solving for variable 'r'. Factor a trinomial. (-4 + -1r)(3 + -5r) = 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 '(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 = {-4, 0.6}
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