Teamwork is not something that just magically happens in matches. Its also a skill thats measured by the ladder (arguably the single most measured skill as well). You don't go into a game as a solo and just randomly have everyone work together like a well oiled machine. You have to BUILD some CHEMISTRY with these players, get everyone to laugh, be loose, have a good time. You have to gameplan with them effectively using what communication tools you have. You have to reassure them when they make mistakes. You have to congratulate them when they do something well.
You don't see a Marine Platoon run into a firefight, say nothing to one another, and just randomly hold down the fort.
You don't see a Football team get into the huddle, have all 11 remain silent, break the huddle, then get to the line of scrimmage and snap the ball and perfectly execute a play.
You don't see a construction crew arrive at a job site, stare at each for a few seconds, and then everyone perform the task they should be doing to build a building or a bridge.
Teamwork requires COMMUNICATION. And the burden for communicating effectively with your team is on you. The reason YOU have difficulty as a solo players is because you LACK a basic skill required to play this game, communicating with your team effectively and being a leader and team organizer. The reason you have success playing with your friends is because they HAVE this skill and make up for your lack of it, which you have been using as a crutch to cover up your weakness as a player.
Start trying to be a positive force starting in lobby when you play solo. Don't get into a lobby and then remain silent. TALK! Crack some jokes, get everyone loose, op.gg everyone and give your teammates an ideal composition with everyone on their best champs and roles. Then get into the game and CONTINUE to do these things. Communicate a strategy and make sure everyone is on the same page so you can execute it. Encourage them when they get down on themselves for making a mistake. Help them, not just with your actions, but also your focus and leadership.
You will, of course, occasionally run into those stubborn people who don't want to work as part of a group. But more often than not players WANT to win and WANT to work together provided they believe they have a chance of WINNING if they do so. GIVE them this chance, and they will fall into step with you.
I have one true talent at this game and it is the sole reason for my being a high diamond player for 4 seasons now. I know how to be a leader and get my teams to function in harmony as a unit. If it were impossible to do this then my silver mechanics would have kept me in low elo this whole time. I literally get by purely on my ability to inspire people to work as a team. Its a skill you need to learn. Its the most important skill to have.