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Simplifying -1[8z + -1(13z + 1)] = 1 + (4z + 0) Reorder the terms: -1[8z + -1(1 + 13z)] = 1 + (4z + 0) -1[8z + (1 * -1 + 13z * -1)] = 1 + (4z + 0) -1[8z + (-1 + -13z)] = 1 + (4z + 0) Reorder the terms: -1[-1 + 8z + -13z] = 1 + (4z + 0) Combine like terms: 8z + -13z = -5z -1[-1 + -5z] = 1 + (4z + 0) [-1 * -1 + -5z * -1] = 1 + (4z + 0) [1 + 5z] = 1 + (4z + 0) Reorder the terms: 1 + 5z = 1 + (0 + 4z) Remove the zero: 1 + 5z = 1 + (4z) 1 + 5z = 1 + (4z) Add '-1' to each side of the equation. 1 + -1 + 5z = 1 + -1 + (4z) Combine like terms: 1 + -1 = 0 0 + 5z = 1 + -1 + (4z) 5z = 1 + -1 + (4z) Combine like terms: 1 + -1 = 0 5z = 0 + (4z) 5z = (4z) Solving 5z = (4z) Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '(-4z)' to each side of the equation. 5z + (-4z) = (4z) + (-4z) Combine like terms: 5z + (-4z) = 1z 1z = (4z) + (-4z) Combine like terms: (4z) + (-4z) = 0 1z = 0 Divide each side by '1'. z = 0 Simplifying z = 0
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