How can I find the roots of the polynomial $12x^{4}+2x^3+10x^2+2x-2$? It's clear that I can divide by $2$, but I don't know what can I do with $$6x^{4}+x^3+5x^2+x-1$$
Is there any algorithm for it or a trick? I have found the roots by an online calculator but I don't know how can I calculate them. Thank you for your help.

Here, I try to give a way of factorization, which isn't too hard to be noticed:
$6x^4+x^3+5x^2+x-1$
$=5x^4+x^3+5x^2+x+x^4-1$
$=x^3(5x+1)+x(5x+1)+(x^2+1)(x^2-1)$
$=x(x^2+1)(5x+1)+(x^2+1)(x^2-1)$
$=(x^2+1)(6x^2+x-1)$
$=(x^2+1)(3x-1)(2x+1)$
