Singing while playing piano

I took piano lessons my whole childhood and this gave me an understanding of how to read music. I have continued to play piano at home because I find it very fun. However, whenever I try to sing and play piano simultaneously I get stumped. At first it is almost impossible but with lots of practice I am sometimes successful. Sometimes I lose patience because it takes so much time to learn how to do this. Some people make it look easy so it is frustrating that it is so difficult. I know these people who have mastered this skill had to practice a lot and have a ton of patience, so I envy them for this achievement. I also have a guitar at home, when I was 13 I picked up the guitar and randomly wrote a little song, I made up all the chords and then I made words to the song. For some odd reason this song ended up somewhat sucessful, I look back on it now and the words seem dumb, but all together it sounded good. After that I kept trying to do more with the guitar while singing. I took some guitar lessons but I wasnt able to do the same thing again, singing and playing guitar takes a ton of practice and it is even more difficult.