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Simplifying (2x + 4y + -3z) + (3y + 2z + 6x) + (4z + -8x + -7y) = 0 Remove parenthesis around (2x + 4y + -3z) 2x + 4y + -3z + (3y + 2z + 6x) + (4z + -8x + -7y) = 0 Reorder the terms: 2x + 4y + -3z + (6x + 3y + 2z) + (4z + -8x + -7y) = 0 Remove parenthesis around (6x + 3y + 2z) 2x + 4y + -3z + 6x + 3y + 2z + (4z + -8x + -7y) = 0 Reorder the terms: 2x + 4y + -3z + 6x + 3y + 2z + (-8x + -7y + 4z) = 0 Remove parenthesis around (-8x + -7y + 4z) 2x + 4y + -3z + 6x + 3y + 2z + -8x + -7y + 4z = 0 Reorder the terms: 2x + 6x + -8x + 4y + 3y + -7y + -3z + 2z + 4z = 0 Combine like terms: 2x + 6x = 8x 8x + -8x + 4y + 3y + -7y + -3z + 2z + 4z = 0 Combine like terms: 8x + -8x = 0 0 + 4y + 3y + -7y + -3z + 2z + 4z = 0 4y + 3y + -7y + -3z + 2z + 4z = 0 Combine like terms: 4y + 3y = 7y 7y + -7y + -3z + 2z + 4z = 0 Combine like terms: 7y + -7y = 0 0 + -3z + 2z + 4z = 0 -3z + 2z + 4z = 0 Combine like terms: -3z + 2z = -1z -1z + 4z = 0 Combine like terms: -1z + 4z = 3z 3z = 0 Solving 3z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Divide each side by '3'. z = 0 Simplifying z = 0
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