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Simplifying -1[5z + -1(12z + 8)] = 8(6z + 1) Reorder the terms: -1[5z + -1(8 + 12z)] = 8(6z + 1) -1[5z + (8 * -1 + 12z * -1)] = 8(6z + 1) -1[5z + (-8 + -12z)] = 8(6z + 1) Reorder the terms: -1[-8 + 5z + -12z] = 8(6z + 1) Combine like terms: 5z + -12z = -7z -1[-8 + -7z] = 8(6z + 1) [-8 * -1 + -7z * -1] = 8(6z + 1) [8 + 7z] = 8(6z + 1) Reorder the terms: 8 + 7z = 8(1 + 6z) 8 + 7z = (1 * 8 + 6z * 8) 8 + 7z = (8 + 48z) Add '-8' to each side of the equation. 8 + -8 + 7z = 8 + -8 + 48z Combine like terms: 8 + -8 = 0 0 + 7z = 8 + -8 + 48z 7z = 8 + -8 + 48z Combine like terms: 8 + -8 = 0 7z = 0 + 48z 7z = 48z Solving 7z = 48z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-48z' to each side of the equation. 7z + -48z = 48z + -48z Combine like terms: 7z + -48z = -41z -41z = 48z + -48z Combine like terms: 48z + -48z = 0 -41z = 0 Divide each side by '-41'. z = 0 Simplifying z = 0
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