Verify that the given differential equation $is$ exact; then solve $it.$

$(6x^2+6y^2)dx+(12xy+9y^2)dy=0$

Select the correct choice below and, $if$ necessary, fill $in$ the answer box $to$ complete your choice.

$A.$ The equation $is$ exact and $an$ implicit solution $in$ the form $F(x,y)=Cis,=C,$ where $Cx$ and $yas$ the variables.