Password Reset Not Working

[Carlos Williams]

I noticed today that I strangely was unable to login to MySQL as root.
I just assumed I forgot the password and decided to reset my root
password:

1 - /etc/init.d/mysqld stop

2 - mysqld_safe --skip-grant-tables &

3 - mysql -u root

4 - mysql> use mysql;

mysql> mysql> update user set password='letmein' where user='root';
Query OK, 2 rows affected (0.00 sec)
Rows matched: 2  Changed: 2  Warnings: 0

mysql> flush privileges;

mysql> quit

5 - /etc/init.d/mysqld restart

*Now after I do all that, I get the following:*

mysql -u root -p
Enter password:
ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using
password: YES)

I have done this over and over and can't login so I am wondering if
something is wrong with MySQL or am I just not properly resetting the
password...

Someone please help!