IAS math problem 2017-paper 1 4a Reduce the following equation into standard form and hence determine the nature of coincoid $x^2+y^2+z^2-zx-xy-yz-3x-6y-9z+21=0$
I have reduced the equation into $(x-3/2)^2 +(y-3)^2 + (z-9/2)^2 -zx -xy-yz = 21/2$ from here on I can sense to reduce it to any of the standard 3D form that I am aware of(like ellipse, ellipsoid, hyperboloid, etc.,). Please help me out in the same.

I got that our equation it's
$$(x-y+7)^2+(y-z+1)^2+(z-x-8)^2=36(x+2).$$
I think from here we can  get $x=-2$, but I don't see this.
