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3x^2+4xy+3z^2+8xz+8yz=0 canonical form

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   2      2                            
3*x  + 3*z  + 4*x*y + 8*x*z + 8*y*z = 0
$$3 x^{2} + 4 x y + 8 x z + 8 y z + 3 z^{2} = 0$$
3*x^2 + 4*x*y + 8*x*z + 8*y*z + 3*z^2 = 0