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Simplifying 2(4z + -5) + 8(3z + 4) = 0 Reorder the terms: 2(-5 + 4z) + 8(3z + 4) = 0 (-5 * 2 + 4z * 2) + 8(3z + 4) = 0 (-10 + 8z) + 8(3z + 4) = 0 Reorder the terms: -10 + 8z + 8(4 + 3z) = 0 -10 + 8z + (4 * 8 + 3z * 8) = 0 -10 + 8z + (32 + 24z) = 0 Reorder the terms: -10 + 32 + 8z + 24z = 0 Combine like terms: -10 + 32 = 22 22 + 8z + 24z = 0 Combine like terms: 8z + 24z = 32z 22 + 32z = 0 Solving 22 + 32z = 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 + 32z = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 32z = 0 + -22 32z = 0 + -22 Combine like terms: 0 + -22 = -22 32z = -22 Divide each side by '32'. z = -0.6875 Simplifying z = -0.6875
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