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Simplifying 4(3z + -6) + 9(5z + 4) = 0 Reorder the terms: 4(-6 + 3z) + 9(5z + 4) = 0 (-6 * 4 + 3z * 4) + 9(5z + 4) = 0 (-24 + 12z) + 9(5z + 4) = 0 Reorder the terms: -24 + 12z + 9(4 + 5z) = 0 -24 + 12z + (4 * 9 + 5z * 9) = 0 -24 + 12z + (36 + 45z) = 0 Reorder the terms: -24 + 36 + 12z + 45z = 0 Combine like terms: -24 + 36 = 12 12 + 12z + 45z = 0 Combine like terms: 12z + 45z = 57z 12 + 57z = 0 Solving 12 + 57z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + 57z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 57z = 0 + -12 57z = 0 + -12 Combine like terms: 0 + -12 = -12 57z = -12 Divide each side by '57'. z = -0.2105263158 Simplifying z = -0.2105263158
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