The differential equation

$\frac{dy}{dx}=24+20x+48y+40xy$

has $an$ implicit general solution $of$ the form $F(x,y)=K,$ where $Kisan$ arbitrary constant.

$In$ 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.

$F(x,y)=G(x)+H(y)=$