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Simplifying 5x + 4y + 7z + -3x + 5z + -6y = 0 Reorder the terms: 5x + -3x + 4y + -6y + 7z + 5z = 0 Combine like terms: 5x + -3x = 2x 2x + 4y + -6y + 7z + 5z = 0 Combine like terms: 4y + -6y = -2y 2x + -2y + 7z + 5z = 0 Combine like terms: 7z + 5z = 12z 2x + -2y + 12z = 0 Solving 2x + -2y + 12z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 2x + -2y + 2y + 12z = 0 + 2y Combine like terms: -2y + 2y = 0 2x + 0 + 12z = 0 + 2y 2x + 12z = 0 + 2y Remove the zero: 2x + 12z = 2y Add '-12z' to each side of the equation. 2x + 12z + -12z = 2y + -12z Combine like terms: 12z + -12z = 0 2x + 0 = 2y + -12z 2x = 2y + -12z Divide each side by '2'. x = y + -6z Simplifying x = y + -6z
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