Exact differential problem

The differential g(x,y)=(10x^2+6xy+6y^2)dx+(9x^2+4xy+15y^2)dy is not exact.

But ( 2x+3y)^m g(x,y) is equal to dz, the exact differential of a function z=f(x,y). Find f(x,y)
Where m=2 (though apparently there is also a way of finding and proving that too..?)

What is the method to solve this to give an answer of f(x,y)= 8x^5+36x^4y+62x^3y^2+63x^2y^3+54xy^4+27y^5+c ?