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