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Simplifying 2(4z + -5) + 8(2z + 4) = 0 Reorder the terms: 2(-5 + 4z) + 8(2z + 4) = 0 (-5 * 2 + 4z * 2) + 8(2z + 4) = 0 (-10 + 8z) + 8(2z + 4) = 0 Reorder the terms: -10 + 8z + 8(4 + 2z) = 0 -10 + 8z + (4 * 8 + 2z * 8) = 0 -10 + 8z + (32 + 16z) = 0 Reorder the terms: -10 + 32 + 8z + 16z = 0 Combine like terms: -10 + 32 = 22 22 + 8z + 16z = 0 Combine like terms: 8z + 16z = 24z 22 + 24z = 0 Solving 22 + 24z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-22' to each side of the equation. 22 + -22 + 24z = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 24z = 0 + -22 24z = 0 + -22 Combine like terms: 0 + -22 = -22 24z = -22 Divide each side by '24'. z = -0.9166666667 Simplifying z = -0.9166666667
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