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Simplifying (2x + 3)(x + -2) = (2x + 1)(x + -4) + 16 Reorder the terms: (3 + 2x)(x + -2) = (2x + 1)(x + -4) + 16 Reorder the terms: (3 + 2x)(-2 + x) = (2x + 1)(x + -4) + 16 Multiply (3 + 2x) * (-2 + x) (3(-2 + x) + 2x * (-2 + x)) = (2x + 1)(x + -4) + 16 ((-2 * 3 + x * 3) + 2x * (-2 + x)) = (2x + 1)(x + -4) + 16 ((-6 + 3x) + 2x * (-2 + x)) = (2x + 1)(x + -4) + 16 (-6 + 3x + (-2 * 2x + x * 2x)) = (2x + 1)(x + -4) + 16 (-6 + 3x + (-4x + 2x2)) = (2x + 1)(x + -4) + 16 Combine like terms: 3x + -4x = -1x (-6 + -1x + 2x2) = (2x + 1)(x + -4) + 16 Reorder the terms: -6 + -1x + 2x2 = (1 + 2x)(x + -4) + 16 Reorder the terms: -6 + -1x + 2x2 = (1 + 2x)(-4 + x) + 16 Multiply (1 + 2x) * (-4 + x) -6 + -1x + 2x2 = (1(-4 + x) + 2x * (-4 + x)) + 16 -6 + -1x + 2x2 = ((-4 * 1 + x * 1) + 2x * (-4 + x)) + 16 -6 + -1x + 2x2 = ((-4 + 1x) + 2x * (-4 + x)) + 16 -6 + -1x + 2x2 = (-4 + 1x + (-4 * 2x + x * 2x)) + 16 -6 + -1x + 2x2 = (-4 + 1x + (-8x + 2x2)) + 16 Combine like terms: 1x + -8x = -7x -6 + -1x + 2x2 = (-4 + -7x + 2x2) + 16 Reorder the terms: -6 + -1x + 2x2 = -4 + 16 + -7x + 2x2 Combine like terms: -4 + 16 = 12 -6 + -1x + 2x2 = 12 + -7x + 2x2 Add '-2x2' to each side of the equation. -6 + -1x + 2x2 + -2x2 = 12 + -7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -1x + 0 = 12 + -7x + 2x2 + -2x2 -6 + -1x = 12 + -7x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -6 + -1x = 12 + -7x + 0 -6 + -1x = 12 + -7x Solving -6 + -1x = 12 + -7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7x' to each side of the equation. -6 + -1x + 7x = 12 + -7x + 7x Combine like terms: -1x + 7x = 6x -6 + 6x = 12 + -7x + 7x Combine like terms: -7x + 7x = 0 -6 + 6x = 12 + 0 -6 + 6x = 12 Add '6' to each side of the equation. -6 + 6 + 6x = 12 + 6 Combine like terms: -6 + 6 = 0 0 + 6x = 12 + 6 6x = 12 + 6 Combine like terms: 12 + 6 = 18 6x = 18 Divide each side by '6'. x = 3 Simplifying x = 3
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