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Simplifying 4(2z + -6) + 8(4z + 5) = 0 Reorder the terms: 4(-6 + 2z) + 8(4z + 5) = 0 (-6 * 4 + 2z * 4) + 8(4z + 5) = 0 (-24 + 8z) + 8(4z + 5) = 0 Reorder the terms: -24 + 8z + 8(5 + 4z) = 0 -24 + 8z + (5 * 8 + 4z * 8) = 0 -24 + 8z + (40 + 32z) = 0 Reorder the terms: -24 + 40 + 8z + 32z = 0 Combine like terms: -24 + 40 = 16 16 + 8z + 32z = 0 Combine like terms: 8z + 32z = 40z 16 + 40z = 0 Solving 16 + 40z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + 40z = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 40z = 0 + -16 40z = 0 + -16 Combine like terms: 0 + -16 = -16 40z = -16 Divide each side by '40'. z = -0.4 Simplifying z = -0.4
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