HOWTO install ffmpeg on Centos 7
Centos is mostly used for servers which means that multimedia-related packages like ffmpeg are either neglected or outright ignored. This means you'll get stuck if you actually need ffmpeg for audio and/or video transcoding on a website or something like that. However, you can haz ffmpeg on Centos 7.x
Forget these solutions
If you've searched for this you've probably come across solutions which propose that you a) add a RPM repository called "Nux" out of Russia or b) get it from RPMForge. If you tried the first solution you've gotten ffmpeg v2.2 which is old and useless and you've gotten a backdoor for Putin. If you went with solution b) you've got ffmpeg v3.4.6 which is, in fact, quite new. A problem with RPMForge's ffmpeg is that it is NOT compiled with libvpx. What this means is that you can not encode VP8 or VP9 video and VP9 is the format you want to (ab)use to allow web browser users to view videos.
The solution is to use a statically compiled ffmpeg
While this isn't ideal it works. And it's the only viable solution since there is no RPM.
You can download a static ffmpeg from https://johnvansickle.com/ffmpeg/ and extract that and use the ffmpeg he provides. It works on Centos. The downside is that you have to trust that the John Van Sickle has not put the virus or the backdoor in it. A brief inspection does not indicate that he has.