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Simplifying (3x + -5)(4x + 1) = (6x + -7)(2x + -1) Reorder the terms: (-5 + 3x)(4x + 1) = (6x + -7)(2x + -1) Reorder the terms: (-5 + 3x)(1 + 4x) = (6x + -7)(2x + -1) Multiply (-5 + 3x) * (1 + 4x) (-5(1 + 4x) + 3x * (1 + 4x)) = (6x + -7)(2x + -1) ((1 * -5 + 4x * -5) + 3x * (1 + 4x)) = (6x + -7)(2x + -1) ((-5 + -20x) + 3x * (1 + 4x)) = (6x + -7)(2x + -1) (-5 + -20x + (1 * 3x + 4x * 3x)) = (6x + -7)(2x + -1) (-5 + -20x + (3x + 12x2)) = (6x + -7)(2x + -1) Combine like terms: -20x + 3x = -17x (-5 + -17x + 12x2) = (6x + -7)(2x + -1) Reorder the terms: -5 + -17x + 12x2 = (-7 + 6x)(2x + -1) Reorder the terms: -5 + -17x + 12x2 = (-7 + 6x)(-1 + 2x) Multiply (-7 + 6x) * (-1 + 2x) -5 + -17x + 12x2 = (-7(-1 + 2x) + 6x * (-1 + 2x)) -5 + -17x + 12x2 = ((-1 * -7 + 2x * -7) + 6x * (-1 + 2x)) -5 + -17x + 12x2 = ((7 + -14x) + 6x * (-1 + 2x)) -5 + -17x + 12x2 = (7 + -14x + (-1 * 6x + 2x * 6x)) -5 + -17x + 12x2 = (7 + -14x + (-6x + 12x2)) Combine like terms: -14x + -6x = -20x -5 + -17x + 12x2 = (7 + -20x + 12x2) Add '-12x2' to each side of the equation. -5 + -17x + 12x2 + -12x2 = 7 + -20x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -5 + -17x + 0 = 7 + -20x + 12x2 + -12x2 -5 + -17x = 7 + -20x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -5 + -17x = 7 + -20x + 0 -5 + -17x = 7 + -20x Solving -5 + -17x = 7 + -20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20x' to each side of the equation. -5 + -17x + 20x = 7 + -20x + 20x Combine like terms: -17x + 20x = 3x -5 + 3x = 7 + -20x + 20x Combine like terms: -20x + 20x = 0 -5 + 3x = 7 + 0 -5 + 3x = 7 Add '5' to each side of the equation. -5 + 5 + 3x = 7 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = 7 + 5 3x = 7 + 5 Combine like terms: 7 + 5 = 12 3x = 12 Divide each side by '3'. x = 4 Simplifying x = 4
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