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Simplifying (x + 1)(2x + 5) = (2x + 3)(x + 4) + 5 Reorder the terms: (1 + x)(2x + 5) = (2x + 3)(x + 4) + 5 Reorder the terms: (1 + x)(5 + 2x) = (2x + 3)(x + 4) + 5 Multiply (1 + x) * (5 + 2x) (1(5 + 2x) + x(5 + 2x)) = (2x + 3)(x + 4) + 5 ((5 * 1 + 2x * 1) + x(5 + 2x)) = (2x + 3)(x + 4) + 5 ((5 + 2x) + x(5 + 2x)) = (2x + 3)(x + 4) + 5 (5 + 2x + (5 * x + 2x * x)) = (2x + 3)(x + 4) + 5 (5 + 2x + (5x + 2x2)) = (2x + 3)(x + 4) + 5 Combine like terms: 2x + 5x = 7x (5 + 7x + 2x2) = (2x + 3)(x + 4) + 5 Reorder the terms: 5 + 7x + 2x2 = (3 + 2x)(x + 4) + 5 Reorder the terms: 5 + 7x + 2x2 = (3 + 2x)(4 + x) + 5 Multiply (3 + 2x) * (4 + x) 5 + 7x + 2x2 = (3(4 + x) + 2x * (4 + x)) + 5 5 + 7x + 2x2 = ((4 * 3 + x * 3) + 2x * (4 + x)) + 5 5 + 7x + 2x2 = ((12 + 3x) + 2x * (4 + x)) + 5 5 + 7x + 2x2 = (12 + 3x + (4 * 2x + x * 2x)) + 5 5 + 7x + 2x2 = (12 + 3x + (8x + 2x2)) + 5 Combine like terms: 3x + 8x = 11x 5 + 7x + 2x2 = (12 + 11x + 2x2) + 5 Reorder the terms: 5 + 7x + 2x2 = 12 + 5 + 11x + 2x2 Combine like terms: 12 + 5 = 17 5 + 7x + 2x2 = 17 + 11x + 2x2 Add '-2x2' to each side of the equation. 5 + 7x + 2x2 + -2x2 = 17 + 11x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 7x + 0 = 17 + 11x + 2x2 + -2x2 5 + 7x = 17 + 11x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 5 + 7x = 17 + 11x + 0 5 + 7x = 17 + 11x Solving 5 + 7x = 17 + 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. 5 + 7x + -11x = 17 + 11x + -11x Combine like terms: 7x + -11x = -4x 5 + -4x = 17 + 11x + -11x Combine like terms: 11x + -11x = 0 5 + -4x = 17 + 0 5 + -4x = 17 Add '-5' to each side of the equation. 5 + -5 + -4x = 17 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 17 + -5 -4x = 17 + -5 Combine like terms: 17 + -5 = 12 -4x = 12 Divide each side by '-4'. x = -3 Simplifying x = -3
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