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Simplifying (2x + 3)(x + -2) = (2x + -1)(x + -1) Reorder the terms: (3 + 2x)(x + -2) = (2x + -1)(x + -1) Reorder the terms: (3 + 2x)(-2 + x) = (2x + -1)(x + -1) Multiply (3 + 2x) * (-2 + x) (3(-2 + x) + 2x * (-2 + x)) = (2x + -1)(x + -1) ((-2 * 3 + x * 3) + 2x * (-2 + x)) = (2x + -1)(x + -1) ((-6 + 3x) + 2x * (-2 + x)) = (2x + -1)(x + -1) (-6 + 3x + (-2 * 2x + x * 2x)) = (2x + -1)(x + -1) (-6 + 3x + (-4x + 2x2)) = (2x + -1)(x + -1) Combine like terms: 3x + -4x = -1x (-6 + -1x + 2x2) = (2x + -1)(x + -1) Reorder the terms: -6 + -1x + 2x2 = (-1 + 2x)(x + -1) Reorder the terms: -6 + -1x + 2x2 = (-1 + 2x)(-1 + x) Multiply (-1 + 2x) * (-1 + x) -6 + -1x + 2x2 = (-1(-1 + x) + 2x * (-1 + x)) -6 + -1x + 2x2 = ((-1 * -1 + x * -1) + 2x * (-1 + x)) -6 + -1x + 2x2 = ((1 + -1x) + 2x * (-1 + x)) -6 + -1x + 2x2 = (1 + -1x + (-1 * 2x + x * 2x)) -6 + -1x + 2x2 = (1 + -1x + (-2x + 2x2)) Combine like terms: -1x + -2x = -3x -6 + -1x + 2x2 = (1 + -3x + 2x2) Add '-2x2' to each side of the equation. -6 + -1x + 2x2 + -2x2 = 1 + -3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -1x + 0 = 1 + -3x + 2x2 + -2x2 -6 + -1x = 1 + -3x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -1x = 1 + -3x + 0 -6 + -1x = 1 + -3x Solving -6 + -1x = 1 + -3x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3x' to each side of the equation. -6 + -1x + 3x = 1 + -3x + 3x Combine like terms: -1x + 3x = 2x -6 + 2x = 1 + -3x + 3x Combine like terms: -3x + 3x = 0 -6 + 2x = 1 + 0 -6 + 2x = 1 Add '6' to each side of the equation. -6 + 6 + 2x = 1 + 6 Combine like terms: -6 + 6 = 0 0 + 2x = 1 + 6 2x = 1 + 6 Combine like terms: 1 + 6 = 7 2x = 7 Divide each side by '2'. x = 3.5 Simplifying x = 3.5
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