You are running CentOS 7. Run this:

systemctl status mysqld.service

If no errors show up, try this:

systemctl restart mysqld.service

If that fails, run this:

for i in `ps auxf|grep mysqld|grep "grep" -v|awk '{print $2}'`; do kill -9 $i; done

Then, run this:

systemctl start mysqld.service

And finally, to ensure it is working:

systemctl status mysqld.service

Reinstalling MySQL might help.
First uninstall,
then delete the /var/lib/mysql and /etc/my.cnf or /etc/my.cnf.rpmsave,
then Restart,
then Install.

Had the same problem.
Use command :

to check if SELinux policy is causing the issue. If so, first check if SELinux policy is enables using command #sestatus. If it shows enabled, than disable it.
To disable,
i)# vi /etc/sysconfig/selinux
ii)change 'SELINUX=enforcing' to 'SELINUX=disabled'
iii)restart linux
iv)check with 'sestatus' and it should show "disabled"

Uninstall and reinstall mysql. It should be working.