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Simplifying (x + 3)(x + 5) + -1(x + 1)(x + 6) + -8 = 0 Reorder the terms: (3 + x)(x + 5) + -1(x + 1)(x + 6) + -8 = 0 Reorder the terms: (3 + x)(5 + x) + -1(x + 1)(x + 6) + -8 = 0 Multiply (3 + x) * (5 + x) (3(5 + x) + x(5 + x)) + -1(x + 1)(x + 6) + -8 = 0 ((5 * 3 + x * 3) + x(5 + x)) + -1(x + 1)(x + 6) + -8 = 0 ((15 + 3x) + x(5 + x)) + -1(x + 1)(x + 6) + -8 = 0 (15 + 3x + (5 * x + x * x)) + -1(x + 1)(x + 6) + -8 = 0 (15 + 3x + (5x + x2)) + -1(x + 1)(x + 6) + -8 = 0 Combine like terms: 3x + 5x = 8x (15 + 8x + x2) + -1(x + 1)(x + 6) + -8 = 0 Reorder the terms: 15 + 8x + x2 + -1(1 + x)(x + 6) + -8 = 0 Reorder the terms: 15 + 8x + x2 + -1(1 + x)(6 + x) + -8 = 0 Multiply (1 + x) * (6 + x) 15 + 8x + x2 + -1(1(6 + x) + x(6 + x)) + -8 = 0 15 + 8x + x2 + -1((6 * 1 + x * 1) + x(6 + x)) + -8 = 0 15 + 8x + x2 + -1((6 + 1x) + x(6 + x)) + -8 = 0 15 + 8x + x2 + -1(6 + 1x + (6 * x + x * x)) + -8 = 0 15 + 8x + x2 + -1(6 + 1x + (6x + x2)) + -8 = 0 Combine like terms: 1x + 6x = 7x 15 + 8x + x2 + -1(6 + 7x + x2) + -8 = 0 15 + 8x + x2 + (6 * -1 + 7x * -1 + x2 * -1) + -8 = 0 15 + 8x + x2 + (-6 + -7x + -1x2) + -8 = 0 Reorder the terms: 15 + -6 + -8 + 8x + -7x + x2 + -1x2 = 0 Combine like terms: 15 + -6 = 9 9 + -8 + 8x + -7x + x2 + -1x2 = 0 Combine like terms: 9 + -8 = 1 1 + 8x + -7x + x2 + -1x2 = 0 Combine like terms: 8x + -7x = 1x 1 + 1x + x2 + -1x2 = 0 Combine like terms: x2 + -1x2 = 0 1 + 1x + 0 = 0 1 + 1x = 0 Solving 1 + 1x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1x = 0 + -1 1x = 0 + -1 Combine like terms: 0 + -1 = -1 1x = -1 Divide each side by '1'. x = -1 Simplifying x = -1
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