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Simplifying 9x + 2y + 6Z + -4x + 3z + -3y = 0 Reorder the terms: 6Z + 9x + -4x + 2y + -3y + 3z = 0 Combine like terms: 9x + -4x = 5x 6Z + 5x + 2y + -3y + 3z = 0 Combine like terms: 2y + -3y = -1y 6Z + 5x + -1y + 3z = 0 Solving 6Z + 5x + -1y + 3z = 0 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-5x' to each side of the equation. 6Z + 5x + -1y + -5x + 3z = 0 + -5x Reorder the terms: 6Z + 5x + -5x + -1y + 3z = 0 + -5x Combine like terms: 5x + -5x = 0 6Z + 0 + -1y + 3z = 0 + -5x 6Z + -1y + 3z = 0 + -5x Remove the zero: 6Z + -1y + 3z = -5x Add 'y' to each side of the equation. 6Z + -1y + y + 3z = -5x + y Combine like terms: -1y + y = 0 6Z + 0 + 3z = -5x + y 6Z + 3z = -5x + y Add '-3z' to each side of the equation. 6Z + 3z + -3z = -5x + y + -3z Combine like terms: 3z + -3z = 0 6Z + 0 = -5x + y + -3z 6Z = -5x + y + -3z Divide each side by '6'. Z = -0.8333333333x + 0.1666666667y + -0.5z Simplifying Z = -0.8333333333x + 0.1666666667y + -0.5z
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