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Simplifying 10(4z + 5) + 6(5z + 4) + 8 = 0 Reorder the terms: 10(5 + 4z) + 6(5z + 4) + 8 = 0 (5 * 10 + 4z * 10) + 6(5z + 4) + 8 = 0 (50 + 40z) + 6(5z + 4) + 8 = 0 Reorder the terms: 50 + 40z + 6(4 + 5z) + 8 = 0 50 + 40z + (4 * 6 + 5z * 6) + 8 = 0 50 + 40z + (24 + 30z) + 8 = 0 Reorder the terms: 50 + 24 + 8 + 40z + 30z = 0 Combine like terms: 50 + 24 = 74 74 + 8 + 40z + 30z = 0 Combine like terms: 74 + 8 = 82 82 + 40z + 30z = 0 Combine like terms: 40z + 30z = 70z 82 + 70z = 0 Solving 82 + 70z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-82' to each side of the equation. 82 + -82 + 70z = 0 + -82 Combine like terms: 82 + -82 = 0 0 + 70z = 0 + -82 70z = 0 + -82 Combine like terms: 0 + -82 = -82 70z = -82 Divide each side by '70'. z = -1.171428571 Simplifying z = -1.171428571
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