Issues with installing mysql

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sudo apt-get install mysql-server-5.5

start: Job failed to start
invoke-rc.d: initscript mysql, action "start" failed.
dpkg: Fehler beim Bearbeiten des Paketes mysql-server-5.5 (--configure):
Unterprozess installiertes post-installation-Skript gab den Fehlerwert 1 zurück
Trigger für libc-bin (2.19-0ubuntu6.6) werden verarbeitet ...
Trigger für ureadahead (0.100.0-16) werden verarbeitet ...
Fehler traten auf beim Bearbeiten von:
mysql-server-5.5
E: Sub-process /usr/bin/dpkg returned an error code (1)

sudo apt-get purge mysql-server mysql-client mysql-common mysql-client-5.5 mysql-server-5.5
sudo apt-get remove libdbd-mysql-perl libmysqlclient18 mysql-client-5.5 mysql-common mysql-server-5.5
sudo apt-get autoremove
sudo rm -R /var/lib/mysql
sudo rm -R /etc/mysql

And install it, I got the same error:

2. MySQL Server im Safe Mode ohne Passworteingabe und ohne Netzwerk starten

MySQL wird nun im Safe Mode ohne Passwortabfrage gestartet. Da nun ohne Passwort auf die Datenbank zugegriffen werden
kann wird zusätzlich mit –skip-networking der Netzwerkzugriff unterbunden (kein muss aber zu empfehlen).

Then running:

sudo mysqld_safe --skip-grant-tables
160219 08:13:05 mysqld_safe Can't log to error log and syslog at the same time. Remove all --log-error
configuration options for --syslog to take effect.
160219 08:13:05 mysqld_safe Logging to '/var/log/mysql/error.log'.
160219 08:13:05 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
160219 08:13:05 mysqld_safe mysqld from pid file /var/run/mysqld/mysqld.pid ended

And looking into /var/log/mysql/error.log:

160219 08:13:05 mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
160219 8:13:05 [Warning] Using unique option prefix key_buffer instead of key_buffer_size is deprecated and
will be removed in a future release. Please use the full name instead.
160219 8:13:05 [Note] /usr/sbin/mysqld (mysqld 5.5.47-0ubuntu0.14.04.1) starting as process 22033 ...
160219 8:13:05 [Warning] Using unique option prefix myisam-recover instead of myisam-recover-options is
deprecated and will be removed in a future release. Please use the full name instead.
160219 8:13:05 [Note] Plugin 'FEDERATED' is disabled.
160219 8:13:05 InnoDB: The InnoDB memory heap is disabled
160219 8:13:05 InnoDB: Mutexes and rw_locks use GCC atomic builtins
160219 8:13:05 InnoDB: Compressed tables use zlib 1.2.8
160219 8:13:05 InnoDB: Using Linux native AIO
/usr/sbin/mysqld: Can't create/write to file '/tmp/ibGu3YIt' (Errcode: 13)
160219 8:13:05 InnoDB: Error: unable to create temporary file; errno: 13
160219 8:13:05 [ERROR] Plugin 'InnoDB' init function returned error.
160219 8:13:05 [ERROR] Plugin 'InnoDB' registration as a STORAGE ENGINE failed.
160219 8:13:05 [ERROR] Unknown/unsupported storage engine: InnoDB
160219 8:13:05 [ERROR] Aborting

160219 8:13:05 [Note] /usr/sbin/mysqld: Shutdown complete

160219 08:13:05 mysqld_safe mysqld from pid file /var/run/mysqld/mysqld.pid ended

The important thing was: /usr/sbin/mysqld: Can't create/write to file '/tmp/ibGu3YIt' (Errcode: 13) and yeah, I don't know why, but /tmp belonged not to the root group. After fixing this, I could work again.