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Simplifying (x + 7)(x + 6) + 12 = (x + 5)(x + 9) Reorder the terms: (7 + x)(x + 6) + 12 = (x + 5)(x + 9) Reorder the terms: (7 + x)(6 + x) + 12 = (x + 5)(x + 9) Multiply (7 + x) * (6 + x) (7(6 + x) + x(6 + x)) + 12 = (x + 5)(x + 9) ((6 * 7 + x * 7) + x(6 + x)) + 12 = (x + 5)(x + 9) ((42 + 7x) + x(6 + x)) + 12 = (x + 5)(x + 9) (42 + 7x + (6 * x + x * x)) + 12 = (x + 5)(x + 9) (42 + 7x + (6x + x2)) + 12 = (x + 5)(x + 9) Combine like terms: 7x + 6x = 13x (42 + 13x + x2) + 12 = (x + 5)(x + 9) Reorder the terms: 42 + 12 + 13x + x2 = (x + 5)(x + 9) Combine like terms: 42 + 12 = 54 54 + 13x + x2 = (x + 5)(x + 9) Reorder the terms: 54 + 13x + x2 = (5 + x)(x + 9) Reorder the terms: 54 + 13x + x2 = (5 + x)(9 + x) Multiply (5 + x) * (9 + x) 54 + 13x + x2 = (5(9 + x) + x(9 + x)) 54 + 13x + x2 = ((9 * 5 + x * 5) + x(9 + x)) 54 + 13x + x2 = ((45 + 5x) + x(9 + x)) 54 + 13x + x2 = (45 + 5x + (9 * x + x * x)) 54 + 13x + x2 = (45 + 5x + (9x + x2)) Combine like terms: 5x + 9x = 14x 54 + 13x + x2 = (45 + 14x + x2) Add '-1x2' to each side of the equation. 54 + 13x + x2 + -1x2 = 45 + 14x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + 13x + 0 = 45 + 14x + x2 + -1x2 54 + 13x = 45 + 14x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 54 + 13x = 45 + 14x + 0 54 + 13x = 45 + 14x Solving 54 + 13x = 45 + 14x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14x' to each side of the equation. 54 + 13x + -14x = 45 + 14x + -14x Combine like terms: 13x + -14x = -1x 54 + -1x = 45 + 14x + -14x Combine like terms: 14x + -14x = 0 54 + -1x = 45 + 0 54 + -1x = 45 Add '-54' to each side of the equation. 54 + -54 + -1x = 45 + -54 Combine like terms: 54 + -54 = 0 0 + -1x = 45 + -54 -1x = 45 + -54 Combine like terms: 45 + -54 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9
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