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Simplifying -1[4z + -1(12z + 1)] = 1 + (7z + 0) Reorder the terms: -1[4z + -1(1 + 12z)] = 1 + (7z + 0) -1[4z + (1 * -1 + 12z * -1)] = 1 + (7z + 0) -1[4z + (-1 + -12z)] = 1 + (7z + 0) Reorder the terms: -1[-1 + 4z + -12z] = 1 + (7z + 0) Combine like terms: 4z + -12z = -8z -1[-1 + -8z] = 1 + (7z + 0) [-1 * -1 + -8z * -1] = 1 + (7z + 0) [1 + 8z] = 1 + (7z + 0) Reorder the terms: 1 + 8z = 1 + (0 + 7z) Remove the zero: 1 + 8z = 1 + (7z) 1 + 8z = 1 + (7z) Add '-1' to each side of the equation. 1 + -1 + 8z = 1 + -1 + (7z) Combine like terms: 1 + -1 = 0 0 + 8z = 1 + -1 + (7z) 8z = 1 + -1 + (7z) Combine like terms: 1 + -1 = 0 8z = 0 + (7z) 8z = (7z) Solving 8z = (7z) Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '(-7z)' to each side of the equation. 8z + (-7z) = (7z) + (-7z) Combine like terms: 8z + (-7z) = 1z 1z = (7z) + (-7z) Combine like terms: (7z) + (-7z) = 0 1z = 0 Divide each side by '1'. z = 0 Simplifying z = 0
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