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Simplifying 12 + 5(2w + 3) = 3(2w + 5) Reorder the terms: 12 + 5(3 + 2w) = 3(2w + 5) 12 + (3 * 5 + 2w * 5) = 3(2w + 5) 12 + (15 + 10w) = 3(2w + 5) Combine like terms: 12 + 15 = 27 27 + 10w = 3(2w + 5) Reorder the terms: 27 + 10w = 3(5 + 2w) 27 + 10w = (5 * 3 + 2w * 3) 27 + 10w = (15 + 6w) Solving 27 + 10w = 15 + 6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6w' to each side of the equation. 27 + 10w + -6w = 15 + 6w + -6w Combine like terms: 10w + -6w = 4w 27 + 4w = 15 + 6w + -6w Combine like terms: 6w + -6w = 0 27 + 4w = 15 + 0 27 + 4w = 15 Add '-27' to each side of the equation. 27 + -27 + 4w = 15 + -27 Combine like terms: 27 + -27 = 0 0 + 4w = 15 + -27 4w = 15 + -27 Combine like terms: 15 + -27 = -12 4w = -12 Divide each side by '4'. w = -3 Simplifying w = -3
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