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Simplifying 3(4z + -7) + 8(2z + 4) = 0 Reorder the terms: 3(-7 + 4z) + 8(2z + 4) = 0 (-7 * 3 + 4z * 3) + 8(2z + 4) = 0 (-21 + 12z) + 8(2z + 4) = 0 Reorder the terms: -21 + 12z + 8(4 + 2z) = 0 -21 + 12z + (4 * 8 + 2z * 8) = 0 -21 + 12z + (32 + 16z) = 0 Reorder the terms: -21 + 32 + 12z + 16z = 0 Combine like terms: -21 + 32 = 11 11 + 12z + 16z = 0 Combine like terms: 12z + 16z = 28z 11 + 28z = 0 Solving 11 + 28z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 28z = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 28z = 0 + -11 28z = 0 + -11 Combine like terms: 0 + -11 = -11 28z = -11 Divide each side by '28'. z = -0.3928571429 Simplifying z = -0.3928571429
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