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Simplifying 6(3z + -2) + 8(2z + 3) = 0 Reorder the terms: 6(-2 + 3z) + 8(2z + 3) = 0 (-2 * 6 + 3z * 6) + 8(2z + 3) = 0 (-12 + 18z) + 8(2z + 3) = 0 Reorder the terms: -12 + 18z + 8(3 + 2z) = 0 -12 + 18z + (3 * 8 + 2z * 8) = 0 -12 + 18z + (24 + 16z) = 0 Reorder the terms: -12 + 24 + 18z + 16z = 0 Combine like terms: -12 + 24 = 12 12 + 18z + 16z = 0 Combine like terms: 18z + 16z = 34z 12 + 34z = 0 Solving 12 + 34z = 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 + 34z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 34z = 0 + -12 34z = 0 + -12 Combine like terms: 0 + -12 = -12 34z = -12 Divide each side by '34'. z = -0.3529411765 Simplifying z = -0.3529411765
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