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Simplifying -3(4 + z) + -5(-2 + z) + 2(11z + 3) = 0 (4 * -3 + z * -3) + -5(-2 + z) + 2(11z + 3) = 0 (-12 + -3z) + -5(-2 + z) + 2(11z + 3) = 0 -12 + -3z + (-2 * -5 + z * -5) + 2(11z + 3) = 0 -12 + -3z + (10 + -5z) + 2(11z + 3) = 0 Reorder the terms: -12 + -3z + 10 + -5z + 2(3 + 11z) = 0 -12 + -3z + 10 + -5z + (3 * 2 + 11z * 2) = 0 -12 + -3z + 10 + -5z + (6 + 22z) = 0 Reorder the terms: -12 + 10 + 6 + -3z + -5z + 22z = 0 Combine like terms: -12 + 10 = -2 -2 + 6 + -3z + -5z + 22z = 0 Combine like terms: -2 + 6 = 4 4 + -3z + -5z + 22z = 0 Combine like terms: -3z + -5z = -8z 4 + -8z + 22z = 0 Combine like terms: -8z + 22z = 14z 4 + 14z = 0 Solving 4 + 14z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 14z = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 14z = 0 + -4 14z = 0 + -4 Combine like terms: 0 + -4 = -4 14z = -4 Divide each side by '14'. z = -0.2857142857 Simplifying z = -0.2857142857
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