The smallest value of $2x^2-2xy+5y^2-6y$ 
Find the smallest value of
$$2x^2-2xy+5y^2-6y$$

What I tried:
I used differentiation to find the answer is $-2$, and I'm looking for another way to solve this question, which is factorization. If I could make that polynomial go into the form of $a(x-t)^2+b(y-v)^2 +c$ then the answer would be $c$. Can you please help me solve it by factorization?

$$2x^2-2xy+5y^2-6y=\frac{1}{2}\left(2x-y\right)^2+\frac{1}{2}\left(3y-2\right)^2+\text{something}\,.$$
