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Simplifying 5w + -2(w + -3z) + 2(7z + -1w) = 0 5w + (w * -2 + -3z * -2) + 2(7z + -1w) = 0 5w + (-2w + 6z) + 2(7z + -1w) = 0 Reorder the terms: 5w + -2w + 6z + 2(-1w + 7z) = 0 5w + -2w + 6z + (-1w * 2 + 7z * 2) = 0 5w + -2w + 6z + (-2w + 14z) = 0 Reorder the terms: 5w + -2w + -2w + 6z + 14z = 0 Combine like terms: 5w + -2w = 3w 3w + -2w + 6z + 14z = 0 Combine like terms: 3w + -2w = 1w 1w + 6z + 14z = 0 Combine like terms: 6z + 14z = 20z 1w + 20z = 0 Solving 1w + 20z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-20z' to each side of the equation. 1w + 20z + -20z = 0 + -20z Combine like terms: 20z + -20z = 0 1w + 0 = 0 + -20z 1w = 0 + -20z Remove the zero: 1w = -20z Divide each side by '1'. w = -20z Simplifying w = -20z
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