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Simplifying (x)(x + 13) = (x + 1)(x + 10) Reorder the terms: x(13 + x) = (x + 1)(x + 10) (13 * x + x * x) = (x + 1)(x + 10) (13x + x2) = (x + 1)(x + 10) Reorder the terms: 13x + x2 = (1 + x)(x + 10) Reorder the terms: 13x + x2 = (1 + x)(10 + x) Multiply (1 + x) * (10 + x) 13x + x2 = (1(10 + x) + x(10 + x)) 13x + x2 = ((10 * 1 + x * 1) + x(10 + x)) 13x + x2 = ((10 + 1x) + x(10 + x)) 13x + x2 = (10 + 1x + (10 * x + x * x)) 13x + x2 = (10 + 1x + (10x + x2)) Combine like terms: 1x + 10x = 11x 13x + x2 = (10 + 11x + x2) Add '-1x2' to each side of the equation. 13x + x2 + -1x2 = 10 + 11x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13x + 0 = 10 + 11x + x2 + -1x2 13x = 10 + 11x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 13x = 10 + 11x + 0 13x = 10 + 11x Solving 13x = 10 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. 13x + -11x = 10 + 11x + -11x Combine like terms: 13x + -11x = 2x 2x = 10 + 11x + -11x Combine like terms: 11x + -11x = 0 2x = 10 + 0 2x = 10 Divide each side by '2'. x = 5 Simplifying x = 5
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