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Simplifying (x + 4)(x + 6) + 8 = x(x + 1) + -13 Reorder the terms: (4 + x)(x + 6) + 8 = x(x + 1) + -13 Reorder the terms: (4 + x)(6 + x) + 8 = x(x + 1) + -13 Multiply (4 + x) * (6 + x) (4(6 + x) + x(6 + x)) + 8 = x(x + 1) + -13 ((6 * 4 + x * 4) + x(6 + x)) + 8 = x(x + 1) + -13 ((24 + 4x) + x(6 + x)) + 8 = x(x + 1) + -13 (24 + 4x + (6 * x + x * x)) + 8 = x(x + 1) + -13 (24 + 4x + (6x + x2)) + 8 = x(x + 1) + -13 Combine like terms: 4x + 6x = 10x (24 + 10x + x2) + 8 = x(x + 1) + -13 Reorder the terms: 24 + 8 + 10x + x2 = x(x + 1) + -13 Combine like terms: 24 + 8 = 32 32 + 10x + x2 = x(x + 1) + -13 Reorder the terms: 32 + 10x + x2 = x(1 + x) + -13 32 + 10x + x2 = (1 * x + x * x) + -13 32 + 10x + x2 = (1x + x2) + -13 Reorder the terms: 32 + 10x + x2 = -13 + 1x + x2 Add '-1x2' to each side of the equation. 32 + 10x + x2 + -1x2 = -13 + 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 32 + 10x + 0 = -13 + 1x + x2 + -1x2 32 + 10x = -13 + 1x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 32 + 10x = -13 + 1x + 0 32 + 10x = -13 + 1x Solving 32 + 10x = -13 + 1x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1x' to each side of the equation. 32 + 10x + -1x = -13 + 1x + -1x Combine like terms: 10x + -1x = 9x 32 + 9x = -13 + 1x + -1x Combine like terms: 1x + -1x = 0 32 + 9x = -13 + 0 32 + 9x = -13 Add '-32' to each side of the equation. 32 + -32 + 9x = -13 + -32 Combine like terms: 32 + -32 = 0 0 + 9x = -13 + -32 9x = -13 + -32 Combine like terms: -13 + -32 = -45 9x = -45 Divide each side by '9'. x = -5 Simplifying x = -5
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