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Simplifying 3(4z + 1) + -4(z + -9) = 0 Reorder the terms: 3(1 + 4z) + -4(z + -9) = 0 (1 * 3 + 4z * 3) + -4(z + -9) = 0 (3 + 12z) + -4(z + -9) = 0 Reorder the terms: 3 + 12z + -4(-9 + z) = 0 3 + 12z + (-9 * -4 + z * -4) = 0 3 + 12z + (36 + -4z) = 0 Reorder the terms: 3 + 36 + 12z + -4z = 0 Combine like terms: 3 + 36 = 39 39 + 12z + -4z = 0 Combine like terms: 12z + -4z = 8z 39 + 8z = 0 Solving 39 + 8z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + 8z = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 8z = 0 + -39 8z = 0 + -39 Combine like terms: 0 + -39 = -39 8z = -39 Divide each side by '8'. z = -4.875 Simplifying z = -4.875
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