MySQL root access from all hosts

I've installed MySQL server on a remote Ubuntu machine. The `root` user is defined in the `mysql.user` table this way: mysql> SELECT host, user, password FROM user WHERE user = 'root'; +------------------+------+-------------------------------------------+ | host | user | password | +------------------+------+-------------------------------------------+ | localhost | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | | ip-10-48-110-188 | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | | 127.0.0.1 | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | | ::1 | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | +------------------+------+-------------------------------------------+ I can access with user `root` from the same remote machine command-line interface using the standard `mysql` client. Now I want to **allow root access from every host on the internet**, so I tried adding following row (it's an exact duplicate of the first row from previous dump, except for the `host` column): mysql> SELECT host, user, password FROM user WHERE host = '%'; +------------------+------+-------------------------------------------+ | host | user | password | +------------------+------+-------------------------------------------+ | % | root | *xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx | +------------------+------+-------------------------------------------+ But my client on my personal PC continues to tell me (I obscured the server IP): > SQL Error (2003): Can't connect to MySQL server on '46.x.x.x' (10061) I can't tell if it's a authentication error or a network error. On the server firewall I enabled port *3306/TCP* for *0.0.0.0/0*, and that's ok for me...