Suggestions on how to keep in-game performance separate from teammates' attitudes?

Hi, I was just wondering what y'all do..

With the past losing spree that I had this week, I came to realize my biggest shortcoming in this game: My teammate's attitudes, not their personal skill, is what affects my playing. When I get teammates who are good people, no matter whether they lose lane or not, I always find myself driven enough to help them solve their problems, and ultimately win the game. However, when I have teammates who are negative in attitude, even if they are remotely skilled, I'll lose the motivation to win.

When faced with negative teammates, I find that the entire team falls apart. Even if we were winning earlier, a flaming teammate will reduce the performance of everyone else. I even find myself wanting to surrender, even when the game can be turned around. I just lose all drive to play and climb, and end up on a losing train.

So my question is... Those with my problem who obviously have made it past it... how do you do it? Do you play with music? Do you mute? I'm a solo player since none of my friends play league. Thanks!