Factoring quartic equation $$x^4+6x^2+25=0$$
How could I factor it into $(x^2-2x+5)(x^2+2x+5)=0$?
I got the result looking into horrible formulas on wikipedia, but I suppose there's a much easier way. Could you help me?

Why not simply replace $x^2$ by $y$. You then end with a quadratic equation in $y$ from which later uou could extract $x$. The solutions of the quadratic are $-3-4 i$ and $-3+4 i$. Taking the square roots, you then obtain $$x=-1 - 2 I$$ $$x=-1 + 2 I$$ $$x=1 - 2 I$$  $$x=1 - 2 I$$.
