Unable to reset root password

[David Embry]

I have an Oracle 6 Linux box running MySQL version 14.14 Dist 5.6.42. I went to connect to my production and my test database and it is telling me that the root password I have been using since installation is incorrect. SQL Workbench will not connect to the databases either due to incorrect password. I have tried resetting the root password using the information from techrepublic and several other instructional pages, but it does not work for me. I stop the database, connect using skip-grant-tables and skip-networking, login as root without a password, and I enter the command to update the password:

update user set authentication_string=password('NEWPASSWORD') where user='root';

And it shows me that the Query OK, 0 rows affected. Rows matched 4, Changed: 0, and Warnings 0.

Most of the articles I find give me the same instructions, but I always get that there are 0 changes. What am I doing wrong?