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Simplifying 2x(x + -4) + -1(2x + 3)(x + -4) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Reorder the terms: 2x(-4 + x) + -1(2x + 3)(x + -4) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) (-4 * 2x + x * 2x) + -1(2x + 3)(x + -4) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) (-8x + 2x2) + -1(2x + 3)(x + -4) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Reorder the terms: -8x + 2x2 + -1(3 + 2x)(x + -4) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Reorder the terms: -8x + 2x2 + -1(3 + 2x)(-4 + x) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Multiply (3 + 2x) * (-4 + x) -8x + 2x2 + -1(3(-4 + x) + 2x * (-4 + x)) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + -1((-4 * 3 + x * 3) + 2x * (-4 + x)) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + -1((-12 + 3x) + 2x * (-4 + x)) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + -1(-12 + 3x + (-4 * 2x + x * 2x)) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + -1(-12 + 3x + (-8x + 2x2)) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Combine like terms: 3x + -8x = -5x -8x + 2x2 + -1(-12 + -5x + 2x2) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + (-12 * -1 + -5x * -1 + 2x2 * -1) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) -8x + 2x2 + (12 + 5x + -2x2) = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Reorder the terms: 12 + -8x + 5x + 2x2 + -2x2 = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Combine like terms: -8x + 5x = -3x 12 + -3x + 2x2 + -2x2 = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Combine like terms: 2x2 + -2x2 = 0 12 + -3x + 0 = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) 12 + -3x = 4x(2x + -3) + -8(1 + -1x)(1 + -1x) Reorder the terms: 12 + -3x = 4x(-3 + 2x) + -8(1 + -1x)(1 + -1x) 12 + -3x = (-3 * 4x + 2x * 4x) + -8(1 + -1x)(1 + -1x) 12 + -3x = (-12x + 8x2) + -8(1 + -1x)(1 + -1x) Multiply (1 + -1x) * (1 + -1x) 12 + -3x = -12x + 8x2 + -8(1(1 + -1x) + -1x * (1 + -1x)) 12 + -3x = -12x + 8x2 + -8((1 * 1 + -1x * 1) + -1x * (1 + -1x)) 12 + -3x = -12x + 8x2 + -8((1 + -1x) + -1x * (1 + -1x)) 12 + -3x = -12x + 8x2 + -8(1 + -1x + (1 * -1x + -1x * -1x)) 12 + -3x = -12x + 8x2 + -8(1 + -1x + (-1x + 1x2)) Combine like terms: -1x + -1x = -2x 12 + -3x = -12x + 8x2 + -8(1 + -2x + 1x2) 12 + -3x = -12x + 8x2 + (1 * -8 + -2x * -8 + 1x2 * -8) 12 + -3x = -12x + 8x2 + (-8 + 16x + -8x2) Reorder the terms: 12 + -3x = -8 + -12x + 16x + 8x2 + -8x2 Combine like terms: -12x + 16x = 4x 12 + -3x = -8 + 4x + 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 12 + -3x = -8 + 4x + 0 12 + -3x = -8 + 4x Solving 12 + -3x = -8 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 12 + -3x + -4x = -8 + 4x + -4x Combine like terms: -3x + -4x = -7x 12 + -7x = -8 + 4x + -4x Combine like terms: 4x + -4x = 0 12 + -7x = -8 + 0 12 + -7x = -8 Add '-12' to each side of the equation. 12 + -12 + -7x = -8 + -12 Combine like terms: 12 + -12 = 0 0 + -7x = -8 + -12 -7x = -8 + -12 Combine like terms: -8 + -12 = -20 -7x = -20 Divide each side by '-7'. x = 2.857142857 Simplifying x = 2.857142857
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