I need to find all numbers
\begin{equation} 6x^2 + 2x \equiv 20 \pmod{513} \end{equation}
and I'm having a trouble since 513 is not prime number
I tried looking for roots but i end up with
\begin{equation} 2(x+2)(3x-5) \equiv 0 \pmod{513} \end{equation}
which lead to nothing in this case.
I also wanted to somehow find a square foirmual of my equation to make it a bit easier but I
failed doing it and now I'm running out off ideas how to solve it.Any help would be much
appreciated.
I found way to write it down as
\begin{equation} (6x+1)^2 \equiv 121 \pmod{513} \end{equation} and then
\begin{equation} 6x \equiv 6 \pmod{19}\\ 6x \equiv 11 \pmod{19}\\ 6x \equiv 12 \pmod{27}\\ 6x \equiv 13 \pmod{27}\\ \end{equation}
but after solving it I get bad answers so is my approach close to right one?