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Simplifying (w + 3)(w + -3) + -1(w + -6)(w + -3) = 0 Reorder the terms: (3 + w)(w + -3) + -1(w + -6)(w + -3) = 0 Reorder the terms: (3 + w)(-3 + w) + -1(w + -6)(w + -3) = 0 Multiply (3 + w) * (-3 + w) (3(-3 + w) + w(-3 + w)) + -1(w + -6)(w + -3) = 0 ((-3 * 3 + w * 3) + w(-3 + w)) + -1(w + -6)(w + -3) = 0 ((-9 + 3w) + w(-3 + w)) + -1(w + -6)(w + -3) = 0 (-9 + 3w + (-3 * w + w * w)) + -1(w + -6)(w + -3) = 0 (-9 + 3w + (-3w + w2)) + -1(w + -6)(w + -3) = 0 Combine like terms: 3w + -3w = 0 (-9 + 0 + w2) + -1(w + -6)(w + -3) = 0 (-9 + w2) + -1(w + -6)(w + -3) = 0 Reorder the terms: -9 + w2 + -1(-6 + w)(w + -3) = 0 Reorder the terms: -9 + w2 + -1(-6 + w)(-3 + w) = 0 Multiply (-6 + w) * (-3 + w) -9 + w2 + -1(-6(-3 + w) + w(-3 + w)) = 0 -9 + w2 + -1((-3 * -6 + w * -6) + w(-3 + w)) = 0 -9 + w2 + -1((18 + -6w) + w(-3 + w)) = 0 -9 + w2 + -1(18 + -6w + (-3 * w + w * w)) = 0 -9 + w2 + -1(18 + -6w + (-3w + w2)) = 0 Combine like terms: -6w + -3w = -9w -9 + w2 + -1(18 + -9w + w2) = 0 -9 + w2 + (18 * -1 + -9w * -1 + w2 * -1) = 0 -9 + w2 + (-18 + 9w + -1w2) = 0 Reorder the terms: -9 + -18 + 9w + w2 + -1w2 = 0 Combine like terms: -9 + -18 = -27 -27 + 9w + w2 + -1w2 = 0 Combine like terms: w2 + -1w2 = 0 -27 + 9w + 0 = 0 -27 + 9w = 0 Solving -27 + 9w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 9w = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 9w = 0 + 27 9w = 0 + 27 Combine like terms: 0 + 27 = 27 9w = 27 Divide each side by '9'. w = 3 Simplifying w = 3
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