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Simplifying -1(12x + -1)(20x + -3) + (120x + 2)(2x + 1) = 8x + 6 Reorder the terms: -1(-1 + 12x)(20x + -3) + (120x + 2)(2x + 1) = 8x + 6 Reorder the terms: -1(-1 + 12x)(-3 + 20x) + (120x + 2)(2x + 1) = 8x + 6 Multiply (-1 + 12x) * (-3 + 20x) -1(-1(-3 + 20x) + 12x * (-3 + 20x)) + (120x + 2)(2x + 1) = 8x + 6 -1((-3 * -1 + 20x * -1) + 12x * (-3 + 20x)) + (120x + 2)(2x + 1) = 8x + 6 -1((3 + -20x) + 12x * (-3 + 20x)) + (120x + 2)(2x + 1) = 8x + 6 -1(3 + -20x + (-3 * 12x + 20x * 12x)) + (120x + 2)(2x + 1) = 8x + 6 -1(3 + -20x + (-36x + 240x2)) + (120x + 2)(2x + 1) = 8x + 6 Combine like terms: -20x + -36x = -56x -1(3 + -56x + 240x2) + (120x + 2)(2x + 1) = 8x + 6 (3 * -1 + -56x * -1 + 240x2 * -1) + (120x + 2)(2x + 1) = 8x + 6 (-3 + 56x + -240x2) + (120x + 2)(2x + 1) = 8x + 6 Reorder the terms: -3 + 56x + -240x2 + (2 + 120x)(2x + 1) = 8x + 6 Reorder the terms: -3 + 56x + -240x2 + (2 + 120x)(1 + 2x) = 8x + 6 Multiply (2 + 120x) * (1 + 2x) -3 + 56x + -240x2 + (2(1 + 2x) + 120x * (1 + 2x)) = 8x + 6 -3 + 56x + -240x2 + ((1 * 2 + 2x * 2) + 120x * (1 + 2x)) = 8x + 6 -3 + 56x + -240x2 + ((2 + 4x) + 120x * (1 + 2x)) = 8x + 6 -3 + 56x + -240x2 + (2 + 4x + (1 * 120x + 2x * 120x)) = 8x + 6 -3 + 56x + -240x2 + (2 + 4x + (120x + 240x2)) = 8x + 6 Combine like terms: 4x + 120x = 124x -3 + 56x + -240x2 + (2 + 124x + 240x2) = 8x + 6 Reorder the terms: -3 + 2 + 56x + 124x + -240x2 + 240x2 = 8x + 6 Combine like terms: -3 + 2 = -1 -1 + 56x + 124x + -240x2 + 240x2 = 8x + 6 Combine like terms: 56x + 124x = 180x -1 + 180x + -240x2 + 240x2 = 8x + 6 Combine like terms: -240x2 + 240x2 = 0 -1 + 180x + 0 = 8x + 6 -1 + 180x = 8x + 6 Reorder the terms: -1 + 180x = 6 + 8x Solving -1 + 180x = 6 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. -1 + 180x + -8x = 6 + 8x + -8x Combine like terms: 180x + -8x = 172x -1 + 172x = 6 + 8x + -8x Combine like terms: 8x + -8x = 0 -1 + 172x = 6 + 0 -1 + 172x = 6 Add '1' to each side of the equation. -1 + 1 + 172x = 6 + 1 Combine like terms: -1 + 1 = 0 0 + 172x = 6 + 1 172x = 6 + 1 Combine like terms: 6 + 1 = 7 172x = 7 Divide each side by '172'. x = 0.04069767442 Simplifying x = 0.04069767442
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