How get another solutions ? f:=exp(x²*(a-x))

I have a problem with finding a interval where parametr "a" is changing.
My funcion:

                 exp(x²(a-x)) for xcR.
I did this, and I don't know what's next.

g:=x->exp(x²(a-x));
dg:=diff(g(x),x);
solve(dg=0,x);
                      0,2/3a
g(0);
g(2/3a);