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Simplifying (4x + -1)(3x + 5) = (6x + -2)(2x + 3) Reorder the terms: (-1 + 4x)(3x + 5) = (6x + -2)(2x + 3) Reorder the terms: (-1 + 4x)(5 + 3x) = (6x + -2)(2x + 3) Multiply (-1 + 4x) * (5 + 3x) (-1(5 + 3x) + 4x * (5 + 3x)) = (6x + -2)(2x + 3) ((5 * -1 + 3x * -1) + 4x * (5 + 3x)) = (6x + -2)(2x + 3) ((-5 + -3x) + 4x * (5 + 3x)) = (6x + -2)(2x + 3) (-5 + -3x + (5 * 4x + 3x * 4x)) = (6x + -2)(2x + 3) (-5 + -3x + (20x + 12x2)) = (6x + -2)(2x + 3) Combine like terms: -3x + 20x = 17x (-5 + 17x + 12x2) = (6x + -2)(2x + 3) Reorder the terms: -5 + 17x + 12x2 = (-2 + 6x)(2x + 3) Reorder the terms: -5 + 17x + 12x2 = (-2 + 6x)(3 + 2x) Multiply (-2 + 6x) * (3 + 2x) -5 + 17x + 12x2 = (-2(3 + 2x) + 6x * (3 + 2x)) -5 + 17x + 12x2 = ((3 * -2 + 2x * -2) + 6x * (3 + 2x)) -5 + 17x + 12x2 = ((-6 + -4x) + 6x * (3 + 2x)) -5 + 17x + 12x2 = (-6 + -4x + (3 * 6x + 2x * 6x)) -5 + 17x + 12x2 = (-6 + -4x + (18x + 12x2)) Combine like terms: -4x + 18x = 14x -5 + 17x + 12x2 = (-6 + 14x + 12x2) Add '-12x2' to each side of the equation. -5 + 17x + 12x2 + -12x2 = -6 + 14x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -5 + 17x + 0 = -6 + 14x + 12x2 + -12x2 -5 + 17x = -6 + 14x + 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -5 + 17x = -6 + 14x + 0 -5 + 17x = -6 + 14x Solving -5 + 17x = -6 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. -5 + 17x + -14x = -6 + 14x + -14x Combine like terms: 17x + -14x = 3x -5 + 3x = -6 + 14x + -14x Combine like terms: 14x + -14x = 0 -5 + 3x = -6 + 0 -5 + 3x = -6 Add '5' to each side of the equation. -5 + 5 + 3x = -6 + 5 Combine like terms: -5 + 5 = 0 0 + 3x = -6 + 5 3x = -6 + 5 Combine like terms: -6 + 5 = -1 3x = -1 Divide each side by '3'. x = -0.3333333333 Simplifying x = -0.3333333333
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