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Simplifying 3x + -2y + 4z + -2z + -2x + -3y + 5z + 6x + 2y + -3z = 0 Reorder the terms: 3x + -2x + 6x + -2y + -3y + 2y + 4z + -2z + 5z + -3z = 0 Combine like terms: 3x + -2x = 1x 1x + 6x + -2y + -3y + 2y + 4z + -2z + 5z + -3z = 0 Combine like terms: 1x + 6x = 7x 7x + -2y + -3y + 2y + 4z + -2z + 5z + -3z = 0 Combine like terms: -2y + -3y = -5y 7x + -5y + 2y + 4z + -2z + 5z + -3z = 0 Combine like terms: -5y + 2y = -3y 7x + -3y + 4z + -2z + 5z + -3z = 0 Combine like terms: 4z + -2z = 2z 7x + -3y + 2z + 5z + -3z = 0 Combine like terms: 2z + 5z = 7z 7x + -3y + 7z + -3z = 0 Combine like terms: 7z + -3z = 4z 7x + -3y + 4z = 0 Solving 7x + -3y + 4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 7x + -3y + 3y + 4z = 0 + 3y Combine like terms: -3y + 3y = 0 7x + 0 + 4z = 0 + 3y 7x + 4z = 0 + 3y Remove the zero: 7x + 4z = 3y Add '-4z' to each side of the equation. 7x + 4z + -4z = 3y + -4z Combine like terms: 4z + -4z = 0 7x + 0 = 3y + -4z 7x = 3y + -4z Divide each side by '7'. x = 0.4285714286y + -0.5714285714z Simplifying x = 0.4285714286y + -0.5714285714z
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