There are a lot of posts around telling you how to update mysql root password. "Simple!," they cry, "just start mysqld_safe, and use mysqladmin …" But wait, what's that? You don't HAVE mysqld_safe? Well the chances are, you've got one of these new fangled systemd systems, where everything is ass backwards.
Then you went and tried to run mysqld as root didn't you? That didn't work either. Read on …