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!