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Simplifying (w + 3)(w + -3) + -1(w + -2)(w + -3) = 0 Reorder the terms: (3 + w)(w + -3) + -1(w + -2)(w + -3) = 0 Reorder the terms: (3 + w)(-3 + w) + -1(w + -2)(w + -3) = 0 Multiply (3 + w) * (-3 + w) (3(-3 + w) + w(-3 + w)) + -1(w + -2)(w + -3) = 0 ((-3 * 3 + w * 3) + w(-3 + w)) + -1(w + -2)(w + -3) = 0 ((-9 + 3w) + w(-3 + w)) + -1(w + -2)(w + -3) = 0 (-9 + 3w + (-3 * w + w * w)) + -1(w + -2)(w + -3) = 0 (-9 + 3w + (-3w + w2)) + -1(w + -2)(w + -3) = 0 Combine like terms: 3w + -3w = 0 (-9 + 0 + w2) + -1(w + -2)(w + -3) = 0 (-9 + w2) + -1(w + -2)(w + -3) = 0 Reorder the terms: -9 + w2 + -1(-2 + w)(w + -3) = 0 Reorder the terms: -9 + w2 + -1(-2 + w)(-3 + w) = 0 Multiply (-2 + w) * (-3 + w) -9 + w2 + -1(-2(-3 + w) + w(-3 + w)) = 0 -9 + w2 + -1((-3 * -2 + w * -2) + w(-3 + w)) = 0 -9 + w2 + -1((6 + -2w) + w(-3 + w)) = 0 -9 + w2 + -1(6 + -2w + (-3 * w + w * w)) = 0 -9 + w2 + -1(6 + -2w + (-3w + w2)) = 0 Combine like terms: -2w + -3w = -5w -9 + w2 + -1(6 + -5w + w2) = 0 -9 + w2 + (6 * -1 + -5w * -1 + w2 * -1) = 0 -9 + w2 + (-6 + 5w + -1w2) = 0 Reorder the terms: -9 + -6 + 5w + w2 + -1w2 = 0 Combine like terms: -9 + -6 = -15 -15 + 5w + w2 + -1w2 = 0 Combine like terms: w2 + -1w2 = 0 -15 + 5w + 0 = 0 -15 + 5w = 0 Solving -15 + 5w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + 5w = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 5w = 0 + 15 5w = 0 + 15 Combine like terms: 0 + 15 = 15 5w = 15 Divide each side by '5'. w = 3 Simplifying w = 3
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