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Simplifying 3w(w) + -1(w + -5)(w + -3) = 2w(w) + 1 Multiply w * w 3w2 + -1(w + -5)(w + -3) = 2w(w) + 1 Reorder the terms: 3w2 + -1(-5 + w)(w + -3) = 2w(w) + 1 Reorder the terms: 3w2 + -1(-5 + w)(-3 + w) = 2w(w) + 1 Multiply (-5 + w) * (-3 + w) 3w2 + -1(-5(-3 + w) + w(-3 + w)) = 2w(w) + 1 3w2 + -1((-3 * -5 + w * -5) + w(-3 + w)) = 2w(w) + 1 3w2 + -1((15 + -5w) + w(-3 + w)) = 2w(w) + 1 3w2 + -1(15 + -5w + (-3 * w + w * w)) = 2w(w) + 1 3w2 + -1(15 + -5w + (-3w + w2)) = 2w(w) + 1 Combine like terms: -5w + -3w = -8w 3w2 + -1(15 + -8w + w2) = 2w(w) + 1 3w2 + (15 * -1 + -8w * -1 + w2 * -1) = 2w(w) + 1 3w2 + (-15 + 8w + -1w2) = 2w(w) + 1 Reorder the terms: -15 + 8w + 3w2 + -1w2 = 2w(w) + 1 Combine like terms: 3w2 + -1w2 = 2w2 -15 + 8w + 2w2 = 2w(w) + 1 Multiply w * w -15 + 8w + 2w2 = 2w2 + 1 Reorder the terms: -15 + 8w + 2w2 = 1 + 2w2 Add '-2w2' to each side of the equation. -15 + 8w + 2w2 + -2w2 = 1 + 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -15 + 8w + 0 = 1 + 2w2 + -2w2 -15 + 8w = 1 + 2w2 + -2w2 Combine like terms: 2w2 + -2w2 = 0 -15 + 8w = 1 + 0 -15 + 8w = 1 Solving -15 + 8w = 1 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 + 8w = 1 + 15 Combine like terms: -15 + 15 = 0 0 + 8w = 1 + 15 8w = 1 + 15 Combine like terms: 1 + 15 = 16 8w = 16 Divide each side by '8'. w = 2 Simplifying w = 2
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