x-2y+3z=0
x^2-4y^2+9z^2+6xz-1998
=(x^2+6xz+9z^2)-4y^2-1998
=(x+3z)^2-4y^2-1998
=(x+3z+2y)(x+3z-2y)-1998
=0-1998
=-1998