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Simplifying x + y + z + w = 0 Reorder the terms: w + x + y + z = 0 Solving w + x + y + z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1x' to each side of the equation. w + x + y + -1x + z = 0 + -1x Reorder the terms: w + x + -1x + y + z = 0 + -1x Combine like terms: x + -1x = 0 w + 0 + y + z = 0 + -1x w + y + z = 0 + -1x Remove the zero: w + y + z = -1x Add '-1y' to each side of the equation. w + y + -1y + z = -1x + -1y Combine like terms: y + -1y = 0 w + 0 + z = -1x + -1y w + z = -1x + -1y Add '-1z' to each side of the equation. w + z + -1z = -1x + -1y + -1z Combine like terms: z + -1z = 0 w + 0 = -1x + -1y + -1z w = -1x + -1y + -1z Simplifying w = -1x + -1y + -1z
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