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Simplifying (8x + -9)(3x + -4) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 Reorder the terms: (-9 + 8x)(3x + -4) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 Reorder the terms: (-9 + 8x)(-4 + 3x) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 Multiply (-9 + 8x) * (-4 + 3x) (-9(-4 + 3x) + 8x * (-4 + 3x)) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 ((-4 * -9 + 3x * -9) + 8x * (-4 + 3x)) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 ((36 + -27x) + 8x * (-4 + 3x)) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 (36 + -27x + (-4 * 8x + 3x * 8x)) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 (36 + -27x + (-32x + 24x2)) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 Combine like terms: -27x + -32x = -59x (36 + -59x + 24x2) + -1(5x + -6)(5x + -6) = (4 + x)(3 + -1x) + -9 Reorder the terms: 36 + -59x + 24x2 + -1(-6 + 5x)(5x + -6) = (4 + x)(3 + -1x) + -9 Reorder the terms: 36 + -59x + 24x2 + -1(-6 + 5x)(-6 + 5x) = (4 + x)(3 + -1x) + -9 Multiply (-6 + 5x) * (-6 + 5x) 36 + -59x + 24x2 + -1(-6(-6 + 5x) + 5x * (-6 + 5x)) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + -1((-6 * -6 + 5x * -6) + 5x * (-6 + 5x)) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + -1((36 + -30x) + 5x * (-6 + 5x)) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + -1(36 + -30x + (-6 * 5x + 5x * 5x)) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + -1(36 + -30x + (-30x + 25x2)) = (4 + x)(3 + -1x) + -9 Combine like terms: -30x + -30x = -60x 36 + -59x + 24x2 + -1(36 + -60x + 25x2) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + (36 * -1 + -60x * -1 + 25x2 * -1) = (4 + x)(3 + -1x) + -9 36 + -59x + 24x2 + (-36 + 60x + -25x2) = (4 + x)(3 + -1x) + -9 Reorder the terms: 36 + -36 + -59x + 60x + 24x2 + -25x2 = (4 + x)(3 + -1x) + -9 Combine like terms: 36 + -36 = 0 0 + -59x + 60x + 24x2 + -25x2 = (4 + x)(3 + -1x) + -9 -59x + 60x + 24x2 + -25x2 = (4 + x)(3 + -1x) + -9 Combine like terms: -59x + 60x = 1x 1x + 24x2 + -25x2 = (4 + x)(3 + -1x) + -9 Combine like terms: 24x2 + -25x2 = -1x2 1x + -1x2 = (4 + x)(3 + -1x) + -9 Multiply (4 + x) * (3 + -1x) 1x + -1x2 = (4(3 + -1x) + x(3 + -1x)) + -9 1x + -1x2 = ((3 * 4 + -1x * 4) + x(3 + -1x)) + -9 1x + -1x2 = ((12 + -4x) + x(3 + -1x)) + -9 1x + -1x2 = (12 + -4x + (3 * x + -1x * x)) + -9 1x + -1x2 = (12 + -4x + (3x + -1x2)) + -9 Combine like terms: -4x + 3x = -1x 1x + -1x2 = (12 + -1x + -1x2) + -9 Reorder the terms: 1x + -1x2 = 12 + -9 + -1x + -1x2 Combine like terms: 12 + -9 = 3 1x + -1x2 = 3 + -1x + -1x2 Add 'x2' to each side of the equation. 1x + -1x2 + x2 = 3 + -1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1x + 0 = 3 + -1x + -1x2 + x2 1x = 3 + -1x + -1x2 + x2 Combine like terms: -1x2 + x2 = 0 1x = 3 + -1x + 0 1x = 3 + -1x Solving 1x = 3 + -1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add 'x' to each side of the equation. 1x + x = 3 + -1x + x Combine like terms: 1x + x = 2x 2x = 3 + -1x + x Combine like terms: -1x + x = 0 2x = 3 + 0 2x = 3 Divide each side by '2'. x = 1.5 Simplifying x = 1.5
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