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Simplifying -1[8z + -1(14z + 1)] = 1 + (5z + 0) Reorder the terms: -1[8z + -1(1 + 14z)] = 1 + (5z + 0) -1[8z + (1 * -1 + 14z * -1)] = 1 + (5z + 0) -1[8z + (-1 + -14z)] = 1 + (5z + 0) Reorder the terms: -1[-1 + 8z + -14z] = 1 + (5z + 0) Combine like terms: 8z + -14z = -6z -1[-1 + -6z] = 1 + (5z + 0) [-1 * -1 + -6z * -1] = 1 + (5z + 0) [1 + 6z] = 1 + (5z + 0) Reorder the terms: 1 + 6z = 1 + (0 + 5z) Remove the zero: 1 + 6z = 1 + (5z) 1 + 6z = 1 + (5z) Add '-1' to each side of the equation. 1 + -1 + 6z = 1 + -1 + (5z) Combine like terms: 1 + -1 = 0 0 + 6z = 1 + -1 + (5z) 6z = 1 + -1 + (5z) Combine like terms: 1 + -1 = 0 6z = 0 + (5z) 6z = (5z) Solving 6z = (5z) Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '(-5z)' to each side of the equation. 6z + (-5z) = (5z) + (-5z) Combine like terms: 6z + (-5z) = 1z 1z = (5z) + (-5z) Combine like terms: (5z) + (-5z) = 0 1z = 0 Divide each side by '1'. z = 0 Simplifying z = 0
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