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Simplifying 3x + -4y + 2z + 5x + 2y + -3z = 0 Reorder the terms: 3x + 5x + -4y + 2y + 2z + -3z = 0 Combine like terms: 3x + 5x = 8x 8x + -4y + 2y + 2z + -3z = 0 Combine like terms: -4y + 2y = -2y 8x + -2y + 2z + -3z = 0 Combine like terms: 2z + -3z = -1z 8x + -2y + -1z = 0 Solving 8x + -2y + -1z = 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. 8x + -2y + 2y + -1z = 0 + 2y Combine like terms: -2y + 2y = 0 8x + 0 + -1z = 0 + 2y 8x + -1z = 0 + 2y Remove the zero: 8x + -1z = 2y Add 'z' to each side of the equation. 8x + -1z + z = 2y + z Combine like terms: -1z + z = 0 8x + 0 = 2y + z 8x = 2y + z Divide each side by '8'. x = 0.25y + 0.125z Simplifying x = 0.25y + 0.125z
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