Polynomial to factorise : $$ 2x^2 + y^2 - 3y = 0 $$
This is what I did but couldn't reach the final factors: $$\ 2x^2 - 2 + y^2 - 3y + 2 = 0 $$ $$\ 2(x-1)(x+1) + (y-2)(y-1) = 0 $$
Now can we infer anything about the factors from the last expression? If not, then what should be the initial way of factorising it?
Ultimately, the equation describes the ellipse $$ \frac{4(y-3/2)^2}{18}+\frac{4x^2}{9}=1 $$ , so the zeros are exactly the set of points {$(x,y)$} in the ellipse described.