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Simplifying 2w(3w + 1) = w(w + -8) + 5w(w + 1) + -17 Reorder the terms: 2w(1 + 3w) = w(w + -8) + 5w(w + 1) + -17 (1 * 2w + 3w * 2w) = w(w + -8) + 5w(w + 1) + -17 (2w + 6w2) = w(w + -8) + 5w(w + 1) + -17 Reorder the terms: 2w + 6w2 = w(-8 + w) + 5w(w + 1) + -17 2w + 6w2 = (-8 * w + w * w) + 5w(w + 1) + -17 2w + 6w2 = (-8w + w2) + 5w(w + 1) + -17 Reorder the terms: 2w + 6w2 = -8w + w2 + 5w(1 + w) + -17 2w + 6w2 = -8w + w2 + (1 * 5w + w * 5w) + -17 2w + 6w2 = -8w + w2 + (5w + 5w2) + -17 Reorder the terms: 2w + 6w2 = -17 + -8w + 5w + w2 + 5w2 Combine like terms: -8w + 5w = -3w 2w + 6w2 = -17 + -3w + w2 + 5w2 Combine like terms: w2 + 5w2 = 6w2 2w + 6w2 = -17 + -3w + 6w2 Add '-6w2' to each side of the equation. 2w + 6w2 + -6w2 = -17 + -3w + 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 2w + 0 = -17 + -3w + 6w2 + -6w2 2w = -17 + -3w + 6w2 + -6w2 Combine like terms: 6w2 + -6w2 = 0 2w = -17 + -3w + 0 2w = -17 + -3w Solving 2w = -17 + -3w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '3w' to each side of the equation. 2w + 3w = -17 + -3w + 3w Combine like terms: 2w + 3w = 5w 5w = -17 + -3w + 3w Combine like terms: -3w + 3w = 0 5w = -17 + 0 5w = -17 Divide each side by '5'. w = -3.4 Simplifying w = -3.4
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