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Simplifying x(x + 40) = (x + 20)(x + 10) Reorder the terms: x(40 + x) = (x + 20)(x + 10) (40 * x + x * x) = (x + 20)(x + 10) (40x + x2) = (x + 20)(x + 10) Reorder the terms: 40x + x2 = (20 + x)(x + 10) Reorder the terms: 40x + x2 = (20 + x)(10 + x) Multiply (20 + x) * (10 + x) 40x + x2 = (20(10 + x) + x(10 + x)) 40x + x2 = ((10 * 20 + x * 20) + x(10 + x)) 40x + x2 = ((200 + 20x) + x(10 + x)) 40x + x2 = (200 + 20x + (10 * x + x * x)) 40x + x2 = (200 + 20x + (10x + x2)) Combine like terms: 20x + 10x = 30x 40x + x2 = (200 + 30x + x2) Add '-1x2' to each side of the equation. 40x + x2 + -1x2 = 200 + 30x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40x + 0 = 200 + 30x + x2 + -1x2 40x = 200 + 30x + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40x = 200 + 30x + 0 40x = 200 + 30x Solving 40x = 200 + 30x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30x' to each side of the equation. 40x + -30x = 200 + 30x + -30x Combine like terms: 40x + -30x = 10x 10x = 200 + 30x + -30x Combine like terms: 30x + -30x = 0 10x = 200 + 0 10x = 200 Divide each side by '10'. x = 20 Simplifying x = 20
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