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Simplifying (x + 5)(x + 7) = (x + 5) * x Reorder the terms: (5 + x)(x + 7) = (x + 5) * x Reorder the terms: (5 + x)(7 + x) = (x + 5) * x Multiply (5 + x) * (7 + x) (5(7 + x) + x(7 + x)) = (x + 5) * x ((7 * 5 + x * 5) + x(7 + x)) = (x + 5) * x ((35 + 5x) + x(7 + x)) = (x + 5) * x (35 + 5x + (7 * x + x * x)) = (x + 5) * x (35 + 5x + (7x + x2)) = (x + 5) * x Combine like terms: 5x + 7x = 12x (35 + 12x + x2) = (x + 5) * x Reorder the terms: 35 + 12x + x2 = (5 + x) * x Reorder the terms for easier multiplication: 35 + 12x + x2 = x(5 + x) 35 + 12x + x2 = (5 * x + x * x) 35 + 12x + x2 = (5x + x2) Add '-1x2' to each side of the equation. 35 + 12x + x2 + -1x2 = 5x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + 12x + 0 = 5x + x2 + -1x2 35 + 12x = 5x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 35 + 12x = 5x + 0 35 + 12x = 5x Solving 35 + 12x = 5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5x' to each side of the equation. 35 + 12x + -5x = 5x + -5x Combine like terms: 12x + -5x = 7x 35 + 7x = 5x + -5x Combine like terms: 5x + -5x = 0 35 + 7x = 0 Add '-35' to each side of the equation. 35 + -35 + 7x = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 7x = 0 + -35 7x = 0 + -35 Combine like terms: 0 + -35 = -35 7x = -35 Divide each side by '7'. x = -5 Simplifying x = -5
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