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Simplifying 3(4z + -6) + 8(3z + 4) = 0 Reorder the terms: 3(-6 + 4z) + 8(3z + 4) = 0 (-6 * 3 + 4z * 3) + 8(3z + 4) = 0 (-18 + 12z) + 8(3z + 4) = 0 Reorder the terms: -18 + 12z + 8(4 + 3z) = 0 -18 + 12z + (4 * 8 + 3z * 8) = 0 -18 + 12z + (32 + 24z) = 0 Reorder the terms: -18 + 32 + 12z + 24z = 0 Combine like terms: -18 + 32 = 14 14 + 12z + 24z = 0 Combine like terms: 12z + 24z = 36z 14 + 36z = 0 Solving 14 + 36z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + 36z = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 36z = 0 + -14 36z = 0 + -14 Combine like terms: 0 + -14 = -14 36z = -14 Divide each side by '36'. z = -0.3888888889 Simplifying z = -0.3888888889
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