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Simplifying 5x + -1(4x + -7)(3x + -5) = 6 + -3(4x + -9)(x + -1) Reorder the terms: 5x + -1(-7 + 4x)(3x + -5) = 6 + -3(4x + -9)(x + -1) Reorder the terms: 5x + -1(-7 + 4x)(-5 + 3x) = 6 + -3(4x + -9)(x + -1) Multiply (-7 + 4x) * (-5 + 3x) 5x + -1(-7(-5 + 3x) + 4x * (-5 + 3x)) = 6 + -3(4x + -9)(x + -1) 5x + -1((-5 * -7 + 3x * -7) + 4x * (-5 + 3x)) = 6 + -3(4x + -9)(x + -1) 5x + -1((35 + -21x) + 4x * (-5 + 3x)) = 6 + -3(4x + -9)(x + -1) 5x + -1(35 + -21x + (-5 * 4x + 3x * 4x)) = 6 + -3(4x + -9)(x + -1) 5x + -1(35 + -21x + (-20x + 12x2)) = 6 + -3(4x + -9)(x + -1) Combine like terms: -21x + -20x = -41x 5x + -1(35 + -41x + 12x2) = 6 + -3(4x + -9)(x + -1) 5x + (35 * -1 + -41x * -1 + 12x2 * -1) = 6 + -3(4x + -9)(x + -1) 5x + (-35 + 41x + -12x2) = 6 + -3(4x + -9)(x + -1) Reorder the terms: -35 + 5x + 41x + -12x2 = 6 + -3(4x + -9)(x + -1) Combine like terms: 5x + 41x = 46x -35 + 46x + -12x2 = 6 + -3(4x + -9)(x + -1) Reorder the terms: -35 + 46x + -12x2 = 6 + -3(-9 + 4x)(x + -1) Reorder the terms: -35 + 46x + -12x2 = 6 + -3(-9 + 4x)(-1 + x) Multiply (-9 + 4x) * (-1 + x) -35 + 46x + -12x2 = 6 + -3(-9(-1 + x) + 4x * (-1 + x)) -35 + 46x + -12x2 = 6 + -3((-1 * -9 + x * -9) + 4x * (-1 + x)) -35 + 46x + -12x2 = 6 + -3((9 + -9x) + 4x * (-1 + x)) -35 + 46x + -12x2 = 6 + -3(9 + -9x + (-1 * 4x + x * 4x)) -35 + 46x + -12x2 = 6 + -3(9 + -9x + (-4x + 4x2)) Combine like terms: -9x + -4x = -13x -35 + 46x + -12x2 = 6 + -3(9 + -13x + 4x2) -35 + 46x + -12x2 = 6 + (9 * -3 + -13x * -3 + 4x2 * -3) -35 + 46x + -12x2 = 6 + (-27 + 39x + -12x2) Combine like terms: 6 + -27 = -21 -35 + 46x + -12x2 = -21 + 39x + -12x2 Add '12x2' to each side of the equation. -35 + 46x + -12x2 + 12x2 = -21 + 39x + -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -35 + 46x + 0 = -21 + 39x + -12x2 + 12x2 -35 + 46x = -21 + 39x + -12x2 + 12x2 Combine like terms: -12x2 + 12x2 = 0 -35 + 46x = -21 + 39x + 0 -35 + 46x = -21 + 39x Solving -35 + 46x = -21 + 39x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39x' to each side of the equation. -35 + 46x + -39x = -21 + 39x + -39x Combine like terms: 46x + -39x = 7x -35 + 7x = -21 + 39x + -39x Combine like terms: 39x + -39x = 0 -35 + 7x = -21 + 0 -35 + 7x = -21 Add '35' to each side of the equation. -35 + 35 + 7x = -21 + 35 Combine like terms: -35 + 35 = 0 0 + 7x = -21 + 35 7x = -21 + 35 Combine like terms: -21 + 35 = 14 7x = 14 Divide each side by '7'. x = 2 Simplifying x = 2
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