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Simplifying (2x + 6y + -3z) + (4x + 6z + -8y) + (x + -3y + z) = 0 Remove parenthesis around (2x + 6y + -3z) 2x + 6y + -3z + (4x + 6z + -8y) + (x + -3y + z) = 0 Reorder the terms: 2x + 6y + -3z + (4x + -8y + 6z) + (x + -3y + z) = 0 Remove parenthesis around (4x + -8y + 6z) 2x + 6y + -3z + 4x + -8y + 6z + (x + -3y + z) = 0 Remove parenthesis around (x + -3y + z) 2x + 6y + -3z + 4x + -8y + 6z + x + -3y + z = 0 Reorder the terms: 2x + 4x + x + 6y + -8y + -3y + -3z + 6z + z = 0 Combine like terms: 2x + 4x = 6x 6x + x + 6y + -8y + -3y + -3z + 6z + z = 0 Combine like terms: 6x + x = 7x 7x + 6y + -8y + -3y + -3z + 6z + z = 0 Combine like terms: 6y + -8y = -2y 7x + -2y + -3y + -3z + 6z + z = 0 Combine like terms: -2y + -3y = -5y 7x + -5y + -3z + 6z + z = 0 Combine like terms: -3z + 6z = 3z 7x + -5y + 3z + z = 0 Combine like terms: 3z + z = 4z 7x + -5y + 4z = 0 Solving 7x + -5y + 4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 7x + -5y + 5y + 4z = 0 + 5y Combine like terms: -5y + 5y = 0 7x + 0 + 4z = 0 + 5y 7x + 4z = 0 + 5y Remove the zero: 7x + 4z = 5y Add '-4z' to each side of the equation. 7x + 4z + -4z = 5y + -4z Combine like terms: 4z + -4z = 0 7x + 0 = 5y + -4z 7x = 5y + -4z Divide each side by '7'. x = 0.7142857143y + -0.5714285714z Simplifying x = 0.7142857143y + -0.5714285714z
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