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Simplifying (x + y)(y + z)(z + x) = 0 Reorder the terms: (x + y)(y + z)(x + z) = 0 Multiply (x + y) * (y + z) (x(y + z) + y(y + z))(x + z) = 0 ((y * x + z * x) + y(y + z))(x + z) = 0 ((xy + xz) + y(y + z))(x + z) = 0 (xy + xz + (y * y + z * y))(x + z) = 0 Reorder the terms: (xy + xz + (yz + y2))(x + z) = 0 (xy + xz + (yz + y2))(x + z) = 0 (xy + xz + yz + y2)(x + z) = 0 Multiply (xy + xz + yz + y2) * (x + z) (xy(x + z) + xz(x + z) + yz(x + z) + y2(x + z)) = 0 ((x * xy + z * xy) + xz(x + z) + yz(x + z) + y2(x + z)) = 0 Reorder the terms: ((xyz + x2y) + xz(x + z) + yz(x + z) + y2(x + z)) = 0 ((xyz + x2y) + xz(x + z) + yz(x + z) + y2(x + z)) = 0 (xyz + x2y + (x * xz + z * xz) + yz(x + z) + y2(x + z)) = 0 Reorder the terms: (xyz + x2y + (xz2 + x2z) + yz(x + z) + y2(x + z)) = 0 (xyz + x2y + (xz2 + x2z) + yz(x + z) + y2(x + z)) = 0 (xyz + x2y + xz2 + x2z + (x * yz + z * yz) + y2(x + z)) = 0 (xyz + x2y + xz2 + x2z + (xyz + yz2) + y2(x + z)) = 0 (xyz + x2y + xz2 + x2z + xyz + yz2 + (x * y2 + z * y2)) = 0 (xyz + x2y + xz2 + x2z + xyz + yz2 + (xy2 + y2z)) = 0 Reorder the terms: (xyz + xyz + xy2 + xz2 + x2y + x2z + yz2 + y2z) = 0 Combine like terms: xyz + xyz = 2xyz (2xyz + xy2 + xz2 + x2y + x2z + yz2 + y2z) = 0 Solving 2xyz + xy2 + xz2 + x2y + x2z + yz2 + y2z = 0 Solving for variable 'x'. The solution to this equation could not be determined.
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