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Simplifying 4(2x + 3y + -4z) = 0 (2x * 4 + 3y * 4 + -4z * 4) = 0 (8x + 12y + -16z) = 0 Solving 8x + 12y + -16z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12y' to each side of the equation. 8x + 12y + -12y + -16z = 0 + -12y Combine like terms: 12y + -12y = 0 8x + 0 + -16z = 0 + -12y 8x + -16z = 0 + -12y Remove the zero: 8x + -16z = -12y Add '16z' to each side of the equation. 8x + -16z + 16z = -12y + 16z Combine like terms: -16z + 16z = 0 8x + 0 = -12y + 16z 8x = -12y + 16z Divide each side by '8'. x = -1.5y + 2z Simplifying x = -1.5y + 2z
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