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Simplifying (x + -3)(x + 5) + -1(x + -3)(x + 4) = 0 Reorder the terms: (-3 + x)(x + 5) + -1(x + -3)(x + 4) = 0 Reorder the terms: (-3 + x)(5 + x) + -1(x + -3)(x + 4) = 0 Multiply (-3 + x) * (5 + x) (-3(5 + x) + x(5 + x)) + -1(x + -3)(x + 4) = 0 ((5 * -3 + x * -3) + x(5 + x)) + -1(x + -3)(x + 4) = 0 ((-15 + -3x) + x(5 + x)) + -1(x + -3)(x + 4) = 0 (-15 + -3x + (5 * x + x * x)) + -1(x + -3)(x + 4) = 0 (-15 + -3x + (5x + x2)) + -1(x + -3)(x + 4) = 0 Combine like terms: -3x + 5x = 2x (-15 + 2x + x2) + -1(x + -3)(x + 4) = 0 Reorder the terms: -15 + 2x + x2 + -1(-3 + x)(x + 4) = 0 Reorder the terms: -15 + 2x + x2 + -1(-3 + x)(4 + x) = 0 Multiply (-3 + x) * (4 + x) -15 + 2x + x2 + -1(-3(4 + x) + x(4 + x)) = 0 -15 + 2x + x2 + -1((4 * -3 + x * -3) + x(4 + x)) = 0 -15 + 2x + x2 + -1((-12 + -3x) + x(4 + x)) = 0 -15 + 2x + x2 + -1(-12 + -3x + (4 * x + x * x)) = 0 -15 + 2x + x2 + -1(-12 + -3x + (4x + x2)) = 0 Combine like terms: -3x + 4x = 1x -15 + 2x + x2 + -1(-12 + 1x + x2) = 0 -15 + 2x + x2 + (-12 * -1 + 1x * -1 + x2 * -1) = 0 -15 + 2x + x2 + (12 + -1x + -1x2) = 0 Reorder the terms: -15 + 12 + 2x + -1x + x2 + -1x2 = 0 Combine like terms: -15 + 12 = -3 -3 + 2x + -1x + x2 + -1x2 = 0 Combine like terms: 2x + -1x = 1x -3 + 1x + x2 + -1x2 = 0 Combine like terms: x2 + -1x2 = 0 -3 + 1x + 0 = 0 -3 + 1x = 0 Solving -3 + 1x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1x = 0 + 3 1x = 0 + 3 Combine like terms: 0 + 3 = 3 1x = 3 Divide each side by '1'. x = 3 Simplifying x = 3
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