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Simplifying (x + 2)(x + 3) + -1(x + -2)(x + 5) = 6 Reorder the terms: (2 + x)(x + 3) + -1(x + -2)(x + 5) = 6 Reorder the terms: (2 + x)(3 + x) + -1(x + -2)(x + 5) = 6 Multiply (2 + x) * (3 + x) (2(3 + x) + x(3 + x)) + -1(x + -2)(x + 5) = 6 ((3 * 2 + x * 2) + x(3 + x)) + -1(x + -2)(x + 5) = 6 ((6 + 2x) + x(3 + x)) + -1(x + -2)(x + 5) = 6 (6 + 2x + (3 * x + x * x)) + -1(x + -2)(x + 5) = 6 (6 + 2x + (3x + x2)) + -1(x + -2)(x + 5) = 6 Combine like terms: 2x + 3x = 5x (6 + 5x + x2) + -1(x + -2)(x + 5) = 6 Reorder the terms: 6 + 5x + x2 + -1(-2 + x)(x + 5) = 6 Reorder the terms: 6 + 5x + x2 + -1(-2 + x)(5 + x) = 6 Multiply (-2 + x) * (5 + x) 6 + 5x + x2 + -1(-2(5 + x) + x(5 + x)) = 6 6 + 5x + x2 + -1((5 * -2 + x * -2) + x(5 + x)) = 6 6 + 5x + x2 + -1((-10 + -2x) + x(5 + x)) = 6 6 + 5x + x2 + -1(-10 + -2x + (5 * x + x * x)) = 6 6 + 5x + x2 + -1(-10 + -2x + (5x + x2)) = 6 Combine like terms: -2x + 5x = 3x 6 + 5x + x2 + -1(-10 + 3x + x2) = 6 6 + 5x + x2 + (-10 * -1 + 3x * -1 + x2 * -1) = 6 6 + 5x + x2 + (10 + -3x + -1x2) = 6 Reorder the terms: 6 + 10 + 5x + -3x + x2 + -1x2 = 6 Combine like terms: 6 + 10 = 16 16 + 5x + -3x + x2 + -1x2 = 6 Combine like terms: 5x + -3x = 2x 16 + 2x + x2 + -1x2 = 6 Combine like terms: x2 + -1x2 = 0 16 + 2x + 0 = 6 16 + 2x = 6 Solving 16 + 2x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 2x = 6 + -16 Combine like terms: 16 + -16 = 0 0 + 2x = 6 + -16 2x = 6 + -16 Combine like terms: 6 + -16 = -10 2x = -10 Divide each side by '2'. x = -5 Simplifying x = -5
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