The differential equation

dy/dx=(6x+9)/(12y^2+16y+6)

has an implicit general solution of the form F(x, y)=K.
In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form
F(x, y)=G(x)+H(y)=K.
Find such a solution and then give the related functions requested.
F(x, y)=G(x)+H(y)=