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Simplifying 4z + -1[4(z + 2) + 2(z + 4)] = 0 Reorder the terms: 4z + -1[4(2 + z) + 2(z + 4)] = 0 4z + -1[(2 * 4 + z * 4) + 2(z + 4)] = 0 4z + -1[(8 + 4z) + 2(z + 4)] = 0 Reorder the terms: 4z + -1[8 + 4z + 2(4 + z)] = 0 4z + -1[8 + 4z + (4 * 2 + z * 2)] = 0 4z + -1[8 + 4z + (8 + 2z)] = 0 Reorder the terms: 4z + -1[8 + 8 + 4z + 2z] = 0 Combine like terms: 8 + 8 = 16 4z + -1[16 + 4z + 2z] = 0 Combine like terms: 4z + 2z = 6z 4z + -1[16 + 6z] = 0 4z + [16 * -1 + 6z * -1] = 0 4z + [-16 + -6z] = 0 Reorder the terms: -16 + 4z + -6z = 0 Combine like terms: 4z + -6z = -2z -16 + -2z = 0 Solving -16 + -2z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + -2z = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2z = 0 + 16 -2z = 0 + 16 Combine like terms: 0 + 16 = 16 -2z = 16 Divide each side by '-2'. z = -8 Simplifying z = -8
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