8(z^2)=(x^2)+(y^2)-6(x*y*z)

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Solution for 8(z^2)=(x^2)+(y^2)-6(x*y*z) equation: 


Simplifying
8(z2) = (x2) + (y2) + -6(x * y * z)
8z2 = x2 + (y2) + -6(x * y * z)
8z2 = x2 + y2 + -6(x * y * z)

Multiply x * y
8z2 = x2 + y2 + -6(xy * z)

Multiply xy * z
8z2 = x2 + y2 + -6(xyz)

Reorder the terms:
8z2 = -6xyz + x2 + y2

Solving
8z2 = -6xyz + x2 + y2

Solving for variable 'z'.

Reorder the terms:
6xyz + -1x2 + -1y2 + 8z2 = -6xyz + x2 + y2 + 6xyz + -1x2 + -1y2

Reorder the terms:
6xyz + -1x2 + -1y2 + 8z2 = -6xyz + 6xyz + x2 + -1x2 + y2 + -1y2

Combine like terms: -6xyz + 6xyz = 0
6xyz + -1x2 + -1y2 + 8z2 = 0 + x2 + -1x2 + y2 + -1y2
6xyz + -1x2 + -1y2 + 8z2 = x2 + -1x2 + y2 + -1y2

Combine like terms: x2 + -1x2 = 0
6xyz + -1x2 + -1y2 + 8z2 = 0 + y2 + -1y2
6xyz + -1x2 + -1y2 + 8z2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
6xyz + -1x2 + -1y2 + 8z2 = 0

The solution to this equation could not be determined.

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