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Simplifying (w + 6)(w + -6) + -1(w + -3)(w + -6) = 0 Reorder the terms: (6 + w)(w + -6) + -1(w + -3)(w + -6) = 0 Reorder the terms: (6 + w)(-6 + w) + -1(w + -3)(w + -6) = 0 Multiply (6 + w) * (-6 + w) (6(-6 + w) + w(-6 + w)) + -1(w + -3)(w + -6) = 0 ((-6 * 6 + w * 6) + w(-6 + w)) + -1(w + -3)(w + -6) = 0 ((-36 + 6w) + w(-6 + w)) + -1(w + -3)(w + -6) = 0 (-36 + 6w + (-6 * w + w * w)) + -1(w + -3)(w + -6) = 0 (-36 + 6w + (-6w + w2)) + -1(w + -3)(w + -6) = 0 Combine like terms: 6w + -6w = 0 (-36 + 0 + w2) + -1(w + -3)(w + -6) = 0 (-36 + w2) + -1(w + -3)(w + -6) = 0 Reorder the terms: -36 + w2 + -1(-3 + w)(w + -6) = 0 Reorder the terms: -36 + w2 + -1(-3 + w)(-6 + w) = 0 Multiply (-3 + w) * (-6 + w) -36 + w2 + -1(-3(-6 + w) + w(-6 + w)) = 0 -36 + w2 + -1((-6 * -3 + w * -3) + w(-6 + w)) = 0 -36 + w2 + -1((18 + -3w) + w(-6 + w)) = 0 -36 + w2 + -1(18 + -3w + (-6 * w + w * w)) = 0 -36 + w2 + -1(18 + -3w + (-6w + w2)) = 0 Combine like terms: -3w + -6w = -9w -36 + w2 + -1(18 + -9w + w2) = 0 -36 + w2 + (18 * -1 + -9w * -1 + w2 * -1) = 0 -36 + w2 + (-18 + 9w + -1w2) = 0 Reorder the terms: -36 + -18 + 9w + w2 + -1w2 = 0 Combine like terms: -36 + -18 = -54 -54 + 9w + w2 + -1w2 = 0 Combine like terms: w2 + -1w2 = 0 -54 + 9w + 0 = 0 -54 + 9w = 0 Solving -54 + 9w = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + 9w = 0 + 54 Combine like terms: -54 + 54 = 0 0 + 9w = 0 + 54 9w = 0 + 54 Combine like terms: 0 + 54 = 54 9w = 54 Divide each side by '9'. w = 6 Simplifying w = 6
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