I've never had a MySQL install go smoothly. Not Mac. Not Windows. And now Linux joins the mess.
I installed mysql-server via Software Manager after a failed attempt with linuxbrew. I can actually run it in terminal, but I have to use
Access denied for user 'root'@'localhost'
Did you install mysql from apt-get install mysql-server ? it probably asked you for a default root password (Ubuntu like systems usually do). If you have forgotten it, have no fear, the password can be reset
Try doing this as linux root (sudo -i), if that doesn't work try
sudo -i sudo mysql
and give it a shot.
Alternatively, sudo, connect to mysql and create another user account with full privileges something like
GRANT ALL ON *.* to someother user identified by ...