To apply any config changes you've made to MySQL (and in general; most Linux services) requires a restart of the service. Rebooting is also an option, but restarting the specific service is quicker. Restarting MySQL should work something like this:

service mysql restart

Also, to connect to MySQL remotely, you'll need to log in as a user with remote access permissions. You can do that either by creating a new user (with remote access permission), or adjusting an existing user. Personally I would recommend a new user, but the Adminer user is another option.

Also worthy of note is that on v15.x, the root MySQL account uses a Linux socket. So the MySQL root account can only be used by the root Linux user via localhost (e.g. commandline). Because it's locked down and only accessible by root from the localhost, it doesn't require a password.