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Simplifying -4(2 + -1x)(x + 1) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) Reorder the terms: -4(2 + -1x)(1 + x) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) Multiply (2 + -1x) * (1 + x) -4(2(1 + x) + -1x * (1 + x)) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) -4((1 * 2 + x * 2) + -1x * (1 + x)) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) -4((2 + 2x) + -1x * (1 + x)) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) -4(2 + 2x + (1 * -1x + x * -1x)) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) -4(2 + 2x + (-1x + -1x2)) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) Combine like terms: 2x + -1x = 1x -4(2 + 1x + -1x2) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) (2 * -4 + 1x * -4 + -1x2 * -4) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) (-8 + -4x + 4x2) = 7(x + 1)(x + -1) + 3(2 + -1x)(x + -1) Reorder the terms: -8 + -4x + 4x2 = 7(1 + x)(x + -1) + 3(2 + -1x)(x + -1) Reorder the terms: -8 + -4x + 4x2 = 7(1 + x)(-1 + x) + 3(2 + -1x)(x + -1) Multiply (1 + x) * (-1 + x) -8 + -4x + 4x2 = 7(1(-1 + x) + x(-1 + x)) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = 7((-1 * 1 + x * 1) + x(-1 + x)) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = 7((-1 + 1x) + x(-1 + x)) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = 7(-1 + 1x + (-1 * x + x * x)) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = 7(-1 + 1x + (-1x + x2)) + 3(2 + -1x)(x + -1) Combine like terms: 1x + -1x = 0 -8 + -4x + 4x2 = 7(-1 + 0 + x2) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = 7(-1 + x2) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = (-1 * 7 + x2 * 7) + 3(2 + -1x)(x + -1) -8 + -4x + 4x2 = (-7 + 7x2) + 3(2 + -1x)(x + -1) Reorder the terms: -8 + -4x + 4x2 = -7 + 7x2 + 3(2 + -1x)(-1 + x) Multiply (2 + -1x) * (-1 + x) -8 + -4x + 4x2 = -7 + 7x2 + 3(2(-1 + x) + -1x * (-1 + x)) -8 + -4x + 4x2 = -7 + 7x2 + 3((-1 * 2 + x * 2) + -1x * (-1 + x)) -8 + -4x + 4x2 = -7 + 7x2 + 3((-2 + 2x) + -1x * (-1 + x)) -8 + -4x + 4x2 = -7 + 7x2 + 3(-2 + 2x + (-1 * -1x + x * -1x)) -8 + -4x + 4x2 = -7 + 7x2 + 3(-2 + 2x + (1x + -1x2)) Combine like terms: 2x + 1x = 3x -8 + -4x + 4x2 = -7 + 7x2 + 3(-2 + 3x + -1x2) -8 + -4x + 4x2 = -7 + 7x2 + (-2 * 3 + 3x * 3 + -1x2 * 3) -8 + -4x + 4x2 = -7 + 7x2 + (-6 + 9x + -3x2) Reorder the terms: -8 + -4x + 4x2 = -7 + -6 + 9x + 7x2 + -3x2 Combine like terms: -7 + -6 = -13 -8 + -4x + 4x2 = -13 + 9x + 7x2 + -3x2 Combine like terms: 7x2 + -3x2 = 4x2 -8 + -4x + 4x2 = -13 + 9x + 4x2 Add '-4x2' to each side of the equation. -8 + -4x + 4x2 + -4x2 = -13 + 9x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8 + -4x + 0 = -13 + 9x + 4x2 + -4x2 -8 + -4x = -13 + 9x + 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -8 + -4x = -13 + 9x + 0 -8 + -4x = -13 + 9x Solving -8 + -4x = -13 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. -8 + -4x + -9x = -13 + 9x + -9x Combine like terms: -4x + -9x = -13x -8 + -13x = -13 + 9x + -9x Combine like terms: 9x + -9x = 0 -8 + -13x = -13 + 0 -8 + -13x = -13 Add '8' to each side of the equation. -8 + 8 + -13x = -13 + 8 Combine like terms: -8 + 8 = 0 0 + -13x = -13 + 8 -13x = -13 + 8 Combine like terms: -13 + 8 = -5 -13x = -5 Divide each side by '-13'. x = 0.3846153846 Simplifying x = 0.3846153846
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