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Simplifying (2x + -2)(3x + -3) = (3x + -1)(2x + 2) Reorder the terms: (-2 + 2x)(3x + -3) = (3x + -1)(2x + 2) Reorder the terms: (-2 + 2x)(-3 + 3x) = (3x + -1)(2x + 2) Multiply (-2 + 2x) * (-3 + 3x) (-2(-3 + 3x) + 2x * (-3 + 3x)) = (3x + -1)(2x + 2) ((-3 * -2 + 3x * -2) + 2x * (-3 + 3x)) = (3x + -1)(2x + 2) ((6 + -6x) + 2x * (-3 + 3x)) = (3x + -1)(2x + 2) (6 + -6x + (-3 * 2x + 3x * 2x)) = (3x + -1)(2x + 2) (6 + -6x + (-6x + 6x2)) = (3x + -1)(2x + 2) Combine like terms: -6x + -6x = -12x (6 + -12x + 6x2) = (3x + -1)(2x + 2) Reorder the terms: 6 + -12x + 6x2 = (-1 + 3x)(2x + 2) Reorder the terms: 6 + -12x + 6x2 = (-1 + 3x)(2 + 2x) Multiply (-1 + 3x) * (2 + 2x) 6 + -12x + 6x2 = (-1(2 + 2x) + 3x * (2 + 2x)) 6 + -12x + 6x2 = ((2 * -1 + 2x * -1) + 3x * (2 + 2x)) 6 + -12x + 6x2 = ((-2 + -2x) + 3x * (2 + 2x)) 6 + -12x + 6x2 = (-2 + -2x + (2 * 3x + 2x * 3x)) 6 + -12x + 6x2 = (-2 + -2x + (6x + 6x2)) Combine like terms: -2x + 6x = 4x 6 + -12x + 6x2 = (-2 + 4x + 6x2) Add '-6x2' to each side of the equation. 6 + -12x + 6x2 + -6x2 = -2 + 4x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 6 + -12x + 0 = -2 + 4x + 6x2 + -6x2 6 + -12x = -2 + 4x + 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 6 + -12x = -2 + 4x + 0 6 + -12x = -2 + 4x Solving 6 + -12x = -2 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 6 + -12x + -4x = -2 + 4x + -4x Combine like terms: -12x + -4x = -16x 6 + -16x = -2 + 4x + -4x Combine like terms: 4x + -4x = 0 6 + -16x = -2 + 0 6 + -16x = -2 Add '-6' to each side of the equation. 6 + -6 + -16x = -2 + -6 Combine like terms: 6 + -6 = 0 0 + -16x = -2 + -6 -16x = -2 + -6 Combine like terms: -2 + -6 = -8 -16x = -8 Divide each side by '-16'. x = 0.5 Simplifying x = 0.5
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