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Simplifying 3z + 6 + 4z + 3 + 5z + 12 = 0 Reorder the terms: 6 + 3 + 12 + 3z + 4z + 5z = 0 Combine like terms: 6 + 3 = 9 9 + 12 + 3z + 4z + 5z = 0 Combine like terms: 9 + 12 = 21 21 + 3z + 4z + 5z = 0 Combine like terms: 3z + 4z = 7z 21 + 7z + 5z = 0 Combine like terms: 7z + 5z = 12z 21 + 12z = 0 Solving 21 + 12z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + 12z = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 12z = 0 + -21 12z = 0 + -21 Combine like terms: 0 + -21 = -21 12z = -21 Divide each side by '12'. z = -1.75 Simplifying z = -1.75
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