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Simplifying 4(3z + -6) + 8(2z + 4) = 0 Reorder the terms: 4(-6 + 3z) + 8(2z + 4) = 0 (-6 * 4 + 3z * 4) + 8(2z + 4) = 0 (-24 + 12z) + 8(2z + 4) = 0 Reorder the terms: -24 + 12z + 8(4 + 2z) = 0 -24 + 12z + (4 * 8 + 2z * 8) = 0 -24 + 12z + (32 + 16z) = 0 Reorder the terms: -24 + 32 + 12z + 16z = 0 Combine like terms: -24 + 32 = 8 8 + 12z + 16z = 0 Combine like terms: 12z + 16z = 28z 8 + 28z = 0 Solving 8 + 28z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 28z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 28z = 0 + -8 28z = 0 + -8 Combine like terms: 0 + -8 = -8 28z = -8 Divide each side by '28'. z = -0.2857142857 Simplifying z = -0.2857142857
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