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Simplifying 2(3x + 2y + -1z) = 0 (3x * 2 + 2y * 2 + -1z * 2) = 0 (6x + 4y + -2z) = 0 Solving 6x + 4y + -2z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 6x + 4y + -4y + -2z = 0 + -4y Combine like terms: 4y + -4y = 0 6x + 0 + -2z = 0 + -4y 6x + -2z = 0 + -4y Remove the zero: 6x + -2z = -4y Add '2z' to each side of the equation. 6x + -2z + 2z = -4y + 2z Combine like terms: -2z + 2z = 0 6x + 0 = -4y + 2z 6x = -4y + 2z Divide each side by '6'. x = -0.6666666667y + 0.3333333333z Simplifying x = -0.6666666667y + 0.3333333333z
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