A lot of press in this part of the world seems to be panicking about the recent German state election results, where the far-right Alternative für Deutschland (AfD) party won major victories in the ex-East German states. And a lot of analyses have been written about "why?"
Now I'm not an expert on recent German history and politics, but I have done a fair bit of reading about East Germany, and I have a pretty well-defined idea of what the problem is (mind you, I could be entirely wrong).
You see, when Germany re-unified in 1989, this was not a joining of equals. The unification was dominated by West Germany. Apart from one detail in traffic regulations, all East German laws disappeared. All East German institutions disappeared, replaced by copies of West German ones for the East part. And sure, der DDR was a dictatorship, so good riddance for a lot of that stuff – but it also had an excellent school and kindergarten systems, queer rights were way ahead of West Germany, etc. After the the unification, people from the ex-DDR have been treated as second-class citizens in many ways – even most analyses of Angela Merkel reflected this, stressing how she had succeeded despite the disadvange of being from the DDR.
Now, on top of this, there was the treatment of Der Linke, the political party that is the successor of the East German ruling party Sozialistische Einheitspartei Deutschlands (SED). Now, despite its origins, Der Linke is pretty much a milquetoast "further left than the Social Democrats" party – not that different from Vasemmistoliitto in Finland, or Vänsterpartiet in Sweden. However, the two major (West) German political parties (Sozialdemokratische Partei, SPD, and Christlich Demokratische Union, CDU) had labeled Der Linke as an "extremist" party, and refused all collaboration with them.
I'm sure I'm simplifying more than a fair bit, but Der Linke was the most popular party in the former East Germany until the mid-2010s. But the message the SPD and CDU were sending to these voters was "you vote wrong, your vote doesn't matter." This, combined with the general poor treatment of people from the ex-DDR, and the fact the standard of living "the east" still lags behind the former West Germany, pretty obviously paved the way for actual extremist parties gaining popularity in the former East Germany.