I'm stuck dealing with a 3 variable equation and I am trying to determine what kind of 3D surface is produced. the equation is:

x + z^2 + y^2 + 6zy = 0

I have done traces and attempted to draw the surface but I need to manipulate the equation to look like one of the standard forms we know. From graphing software I believe the surface created is a hyperbolic paraboloid which means the above equation should look something like...

z/c = x^2/a^2 - y^2/b^2 which is the standard form of the hyperbolic.

Ive tried completing the square to get rid of the xy term but still end up with an equation that is not close to the standard form. Any suggestions would be greatly appreciated!