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Simplifying 5z + 2[3(1 + -1z) + -2(1 + z)] = 12 5z + 2[(1 * 3 + -1z * 3) + -2(1 + z)] = 12 5z + 2[(3 + -3z) + -2(1 + z)] = 12 5z + 2[3 + -3z + (1 * -2 + z * -2)] = 12 5z + 2[3 + -3z + (-2 + -2z)] = 12 Reorder the terms: 5z + 2[3 + -2 + -3z + -2z] = 12 Combine like terms: 3 + -2 = 1 5z + 2[1 + -3z + -2z] = 12 Combine like terms: -3z + -2z = -5z 5z + 2[1 + -5z] = 12 5z + [1 * 2 + -5z * 2] = 12 5z + [2 + -10z] = 12 Reorder the terms: 2 + 5z + -10z = 12 Combine like terms: 5z + -10z = -5z 2 + -5z = 12 Solving 2 + -5z = 12 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5z = 12 + -2 Combine like terms: 2 + -2 = 0 0 + -5z = 12 + -2 -5z = 12 + -2 Combine like terms: 12 + -2 = 10 -5z = 10 Divide each side by '-5'. z = -2 Simplifying z = -2
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