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Simplifying (x + 2)(x + 7) = (x + 3)(x + 2) Reorder the terms: (2 + x)(x + 7) = (x + 3)(x + 2) Reorder the terms: (2 + x)(7 + x) = (x + 3)(x + 2) Multiply (2 + x) * (7 + x) (2(7 + x) + x(7 + x)) = (x + 3)(x + 2) ((7 * 2 + x * 2) + x(7 + x)) = (x + 3)(x + 2) ((14 + 2x) + x(7 + x)) = (x + 3)(x + 2) (14 + 2x + (7 * x + x * x)) = (x + 3)(x + 2) (14 + 2x + (7x + x2)) = (x + 3)(x + 2) Combine like terms: 2x + 7x = 9x (14 + 9x + x2) = (x + 3)(x + 2) Reorder the terms: 14 + 9x + x2 = (3 + x)(x + 2) Reorder the terms: 14 + 9x + x2 = (3 + x)(2 + x) Multiply (3 + x) * (2 + x) 14 + 9x + x2 = (3(2 + x) + x(2 + x)) 14 + 9x + x2 = ((2 * 3 + x * 3) + x(2 + x)) 14 + 9x + x2 = ((6 + 3x) + x(2 + x)) 14 + 9x + x2 = (6 + 3x + (2 * x + x * x)) 14 + 9x + x2 = (6 + 3x + (2x + x2)) Combine like terms: 3x + 2x = 5x 14 + 9x + x2 = (6 + 5x + x2) Add '-1x2' to each side of the equation. 14 + 9x + x2 + -1x2 = 6 + 5x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14 + 9x + 0 = 6 + 5x + x2 + -1x2 14 + 9x = 6 + 5x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 14 + 9x = 6 + 5x + 0 14 + 9x = 6 + 5x Solving 14 + 9x = 6 + 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. 14 + 9x + -5x = 6 + 5x + -5x Combine like terms: 9x + -5x = 4x 14 + 4x = 6 + 5x + -5x Combine like terms: 5x + -5x = 0 14 + 4x = 6 + 0 14 + 4x = 6 Add '-14' to each side of the equation. 14 + -14 + 4x = 6 + -14 Combine like terms: 14 + -14 = 0 0 + 4x = 6 + -14 4x = 6 + -14 Combine like terms: 6 + -14 = -8 4x = -8 Divide each side by '4'. x = -2 Simplifying x = -2
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