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Simplifying 3(4z + 7) + -4(5z + -9) + -16z = 0 Reorder the terms: 3(7 + 4z) + -4(5z + -9) + -16z = 0 (7 * 3 + 4z * 3) + -4(5z + -9) + -16z = 0 (21 + 12z) + -4(5z + -9) + -16z = 0 Reorder the terms: 21 + 12z + -4(-9 + 5z) + -16z = 0 21 + 12z + (-9 * -4 + 5z * -4) + -16z = 0 21 + 12z + (36 + -20z) + -16z = 0 Reorder the terms: 21 + 36 + 12z + -20z + -16z = 0 Combine like terms: 21 + 36 = 57 57 + 12z + -20z + -16z = 0 Combine like terms: 12z + -20z = -8z 57 + -8z + -16z = 0 Combine like terms: -8z + -16z = -24z 57 + -24z = 0 Solving 57 + -24z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-57' to each side of the equation. 57 + -57 + -24z = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -24z = 0 + -57 -24z = 0 + -57 Combine like terms: 0 + -57 = -57 -24z = -57 Divide each side by '-24'. z = 2.375 Simplifying z = 2.375
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