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Simplifying 5x + 2y + 5z + -3x + 4z + -6y = 0 Reorder the terms: 5x + -3x + 2y + -6y + 5z + 4z = 0 Combine like terms: 5x + -3x = 2x 2x + 2y + -6y + 5z + 4z = 0 Combine like terms: 2y + -6y = -4y 2x + -4y + 5z + 4z = 0 Combine like terms: 5z + 4z = 9z 2x + -4y + 9z = 0 Solving 2x + -4y + 9z = 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. 2x + -4y + 4y + 9z = 0 + 4y Combine like terms: -4y + 4y = 0 2x + 0 + 9z = 0 + 4y 2x + 9z = 0 + 4y Remove the zero: 2x + 9z = 4y Add '-9z' to each side of the equation. 2x + 9z + -9z = 4y + -9z Combine like terms: 9z + -9z = 0 2x + 0 = 4y + -9z 2x = 4y + -9z Divide each side by '2'. x = 2y + -4.5z Simplifying x = 2y + -4.5z
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