MYSQL: ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

1) /etc/init.d/mysqld stop

2) mysqld_safe --skip-grant-tables &

3) mysql -u root

4) Setup new MySQL root user password
use mysql;
#update user set password=PASSWORD("123456") where User='root';
#update mysql.user set password=PASSWORD("123456") where user='root';
update mysql.user set authentication_string=password('123qwe') where user='root' and Host ='localhost';

flush privileges;
quit

5) Stop MySQL Server: /etc/init.d/mysqld stop

6) Start MySQL server and test it:

/etc/init.d/mysqld start

mysql -u root -p