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Simplifying 4x + 2y + 6z + -2x + 2z + -5y = 0 Reorder the terms: 4x + -2x + 2y + -5y + 6z + 2z = 0 Combine like terms: 4x + -2x = 2x 2x + 2y + -5y + 6z + 2z = 0 Combine like terms: 2y + -5y = -3y 2x + -3y + 6z + 2z = 0 Combine like terms: 6z + 2z = 8z 2x + -3y + 8z = 0 Solving 2x + -3y + 8z = 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. 2x + -3y + 3y + 8z = 0 + 3y Combine like terms: -3y + 3y = 0 2x + 0 + 8z = 0 + 3y 2x + 8z = 0 + 3y Remove the zero: 2x + 8z = 3y Add '-8z' to each side of the equation. 2x + 8z + -8z = 3y + -8z Combine like terms: 8z + -8z = 0 2x + 0 = 3y + -8z 2x = 3y + -8z Divide each side by '2'. x = 1.5y + -4z Simplifying x = 1.5y + -4z
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