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Simplifying (x + 3)(2x + 5) = (2x + 1)(x + 7) Reorder the terms: (3 + x)(2x + 5) = (2x + 1)(x + 7) Reorder the terms: (3 + x)(5 + 2x) = (2x + 1)(x + 7) Multiply (3 + x) * (5 + 2x) (3(5 + 2x) + x(5 + 2x)) = (2x + 1)(x + 7) ((5 * 3 + 2x * 3) + x(5 + 2x)) = (2x + 1)(x + 7) ((15 + 6x) + x(5 + 2x)) = (2x + 1)(x + 7) (15 + 6x + (5 * x + 2x * x)) = (2x + 1)(x + 7) (15 + 6x + (5x + 2x2)) = (2x + 1)(x + 7) Combine like terms: 6x + 5x = 11x (15 + 11x + 2x2) = (2x + 1)(x + 7) Reorder the terms: 15 + 11x + 2x2 = (1 + 2x)(x + 7) Reorder the terms: 15 + 11x + 2x2 = (1 + 2x)(7 + x) Multiply (1 + 2x) * (7 + x) 15 + 11x + 2x2 = (1(7 + x) + 2x * (7 + x)) 15 + 11x + 2x2 = ((7 * 1 + x * 1) + 2x * (7 + x)) 15 + 11x + 2x2 = ((7 + 1x) + 2x * (7 + x)) 15 + 11x + 2x2 = (7 + 1x + (7 * 2x + x * 2x)) 15 + 11x + 2x2 = (7 + 1x + (14x + 2x2)) Combine like terms: 1x + 14x = 15x 15 + 11x + 2x2 = (7 + 15x + 2x2) Add '-2x2' to each side of the equation. 15 + 11x + 2x2 + -2x2 = 7 + 15x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + 11x + 0 = 7 + 15x + 2x2 + -2x2 15 + 11x = 7 + 15x + 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 15 + 11x = 7 + 15x + 0 15 + 11x = 7 + 15x Solving 15 + 11x = 7 + 15x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15x' to each side of the equation. 15 + 11x + -15x = 7 + 15x + -15x Combine like terms: 11x + -15x = -4x 15 + -4x = 7 + 15x + -15x Combine like terms: 15x + -15x = 0 15 + -4x = 7 + 0 15 + -4x = 7 Add '-15' to each side of the equation. 15 + -15 + -4x = 7 + -15 Combine like terms: 15 + -15 = 0 0 + -4x = 7 + -15 -4x = 7 + -15 Combine like terms: 7 + -15 = -8 -4x = -8 Divide each side by '-4'. x = 2 Simplifying x = 2
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