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Simplifying (4x + 8)(-1x + 4) + -1(4x + 8)(x + 5) = 0 Reorder the terms: (8 + 4x)(-1x + 4) + -1(4x + 8)(x + 5) = 0 Reorder the terms: (8 + 4x)(4 + -1x) + -1(4x + 8)(x + 5) = 0 Multiply (8 + 4x) * (4 + -1x) (8(4 + -1x) + 4x * (4 + -1x)) + -1(4x + 8)(x + 5) = 0 ((4 * 8 + -1x * 8) + 4x * (4 + -1x)) + -1(4x + 8)(x + 5) = 0 ((32 + -8x) + 4x * (4 + -1x)) + -1(4x + 8)(x + 5) = 0 (32 + -8x + (4 * 4x + -1x * 4x)) + -1(4x + 8)(x + 5) = 0 (32 + -8x + (16x + -4x2)) + -1(4x + 8)(x + 5) = 0 Combine like terms: -8x + 16x = 8x (32 + 8x + -4x2) + -1(4x + 8)(x + 5) = 0 Reorder the terms: 32 + 8x + -4x2 + -1(8 + 4x)(x + 5) = 0 Reorder the terms: 32 + 8x + -4x2 + -1(8 + 4x)(5 + x) = 0 Multiply (8 + 4x) * (5 + x) 32 + 8x + -4x2 + -1(8(5 + x) + 4x * (5 + x)) = 0 32 + 8x + -4x2 + -1((5 * 8 + x * 8) + 4x * (5 + x)) = 0 32 + 8x + -4x2 + -1((40 + 8x) + 4x * (5 + x)) = 0 32 + 8x + -4x2 + -1(40 + 8x + (5 * 4x + x * 4x)) = 0 32 + 8x + -4x2 + -1(40 + 8x + (20x + 4x2)) = 0 Combine like terms: 8x + 20x = 28x 32 + 8x + -4x2 + -1(40 + 28x + 4x2) = 0 32 + 8x + -4x2 + (40 * -1 + 28x * -1 + 4x2 * -1) = 0 32 + 8x + -4x2 + (-40 + -28x + -4x2) = 0 Reorder the terms: 32 + -40 + 8x + -28x + -4x2 + -4x2 = 0 Combine like terms: 32 + -40 = -8 -8 + 8x + -28x + -4x2 + -4x2 = 0 Combine like terms: 8x + -28x = -20x -8 + -20x + -4x2 + -4x2 = 0 Combine like terms: -4x2 + -4x2 = -8x2 -8 + -20x + -8x2 = 0 Solving -8 + -20x + -8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-4'. -4(2 + 5x + 2x2) = 0 Factor a trinomial. -4((2 + x)(1 + 2x)) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve: Simplifying 1 + 2x = 0 Solving 1 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2x = 0 + -1 2x = 0 + -1 Combine like terms: 0 + -1 = -1 2x = -1 Divide each side by '2'. x = -0.5 Simplifying x = -0.5Solution
x = {-2, -0.5}
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