notice that the degree of y is 2 or 4, we can let .

consider the left hand side as a quadratical polynomial of t , we can rewrite it as

.

then factorise :

since the root of is 0 , 1(multiple root) , 4, we have .

then we find the fact that is exactly the sum of .

therefore the factorization follows immediately.

I hope I've made myself clear enough, and can help you out. Good luck!