This is not exactly a question, but I struggled to find a source which would provide “live search” for the whole table and not only the column. There was one ticket open in Feb 2016 that suggested to use hiddenRows to solve this issue and I also found one blog that was implementing this feature, but I don’t think it was the best practice. (http://my-waking-dream.blogspot.com/2013/12/live-search-filter-for-jquery.html#1)
I decided to create my own and would like to share it with people who want to do the same thing.
This is an example, feel free to use it 
https://jsfiddle.net/nvacheishvili/xutkLwod/1/