I'm having trouble solving the following equality: $$x^5 + 25x^4 + 250x^3 + 1250x^2 + 3124x + 3120 $$ $$=$$ $$ax^5 + (b+c)x^4 +(10c+3d)x^3 + (d(b+c))x^2 + (24a+62d)x + 104e$$
It's supposed to end up in an augmented matrix form, so I can solve it with gaussian elimination and the likes, but it has been forever since I've dealt with this. Any tips on how to begin? I also couldn't think of more relevant search topics, so I apologize.
I recall something to do with, instead of just equating the coefficients of the terms with the same exponents, I should instead factor out the variables I want to find out. So I did that, but couldn't go much further.