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Simplifying 4z + 4 + 6z + 13 + 23 + 5z = 0 Reorder the terms: 4 + 13 + 23 + 4z + 6z + 5z = 0 Combine like terms: 4 + 13 = 17 17 + 23 + 4z + 6z + 5z = 0 Combine like terms: 17 + 23 = 40 40 + 4z + 6z + 5z = 0 Combine like terms: 4z + 6z = 10z 40 + 10z + 5z = 0 Combine like terms: 10z + 5z = 15z 40 + 15z = 0 Solving 40 + 15z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + 15z = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 15z = 0 + -40 15z = 0 + -40 Combine like terms: 0 + -40 = -40 15z = -40 Divide each side by '15'. z = -2.666666667 Simplifying z = -2.666666667
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