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Simplifying (9x + -4)(2x + -6) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 Reorder the terms: (-4 + 9x)(2x + -6) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 Reorder the terms: (-4 + 9x)(-6 + 2x) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 Multiply (-4 + 9x) * (-6 + 2x) (-4(-6 + 2x) + 9x * (-6 + 2x)) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 ((-6 * -4 + 2x * -4) + 9x * (-6 + 2x)) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 ((24 + -8x) + 9x * (-6 + 2x)) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 (24 + -8x + (-6 * 9x + 2x * 9x)) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 (24 + -8x + (-54x + 18x2)) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 Combine like terms: -8x + -54x = -62x (24 + -62x + 18x2) + (7x + -3)(x + 5) + -1(5x + 3)(5x + 1) = 4 Reorder the terms: 24 + -62x + 18x2 + (-3 + 7x)(x + 5) + -1(5x + 3)(5x + 1) = 4 Reorder the terms: 24 + -62x + 18x2 + (-3 + 7x)(5 + x) + -1(5x + 3)(5x + 1) = 4 Multiply (-3 + 7x) * (5 + x) 24 + -62x + 18x2 + (-3(5 + x) + 7x * (5 + x)) + -1(5x + 3)(5x + 1) = 4 24 + -62x + 18x2 + ((5 * -3 + x * -3) + 7x * (5 + x)) + -1(5x + 3)(5x + 1) = 4 24 + -62x + 18x2 + ((-15 + -3x) + 7x * (5 + x)) + -1(5x + 3)(5x + 1) = 4 24 + -62x + 18x2 + (-15 + -3x + (5 * 7x + x * 7x)) + -1(5x + 3)(5x + 1) = 4 24 + -62x + 18x2 + (-15 + -3x + (35x + 7x2)) + -1(5x + 3)(5x + 1) = 4 Combine like terms: -3x + 35x = 32x 24 + -62x + 18x2 + (-15 + 32x + 7x2) + -1(5x + 3)(5x + 1) = 4 Reorder the terms: 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3 + 5x)(5x + 1) = 4 Reorder the terms: 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3 + 5x)(1 + 5x) = 4 Multiply (3 + 5x) * (1 + 5x) 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3(1 + 5x) + 5x * (1 + 5x)) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1((1 * 3 + 5x * 3) + 5x * (1 + 5x)) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1((3 + 15x) + 5x * (1 + 5x)) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3 + 15x + (1 * 5x + 5x * 5x)) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3 + 15x + (5x + 25x2)) = 4 Combine like terms: 15x + 5x = 20x 24 + -62x + 18x2 + -15 + 32x + 7x2 + -1(3 + 20x + 25x2) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + (3 * -1 + 20x * -1 + 25x2 * -1) = 4 24 + -62x + 18x2 + -15 + 32x + 7x2 + (-3 + -20x + -25x2) = 4 Reorder the terms: 24 + -15 + -3 + -62x + 32x + -20x + 18x2 + 7x2 + -25x2 = 4 Combine like terms: 24 + -15 = 9 9 + -3 + -62x + 32x + -20x + 18x2 + 7x2 + -25x2 = 4 Combine like terms: 9 + -3 = 6 6 + -62x + 32x + -20x + 18x2 + 7x2 + -25x2 = 4 Combine like terms: -62x + 32x = -30x 6 + -30x + -20x + 18x2 + 7x2 + -25x2 = 4 Combine like terms: -30x + -20x = -50x 6 + -50x + 18x2 + 7x2 + -25x2 = 4 Combine like terms: 18x2 + 7x2 = 25x2 6 + -50x + 25x2 + -25x2 = 4 Combine like terms: 25x2 + -25x2 = 0 6 + -50x + 0 = 4 6 + -50x = 4 Solving 6 + -50x = 4 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -50x = 4 + -6 Combine like terms: 6 + -6 = 0 0 + -50x = 4 + -6 -50x = 4 + -6 Combine like terms: 4 + -6 = -2 -50x = -2 Divide each side by '-50'. x = 0.04 Simplifying x = 0.04
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