Some players say after level 20 it’s very hard to solo and some case they can not.

    Once you get to about esteldin you will find that you will need a group for nearly all the quests. And once you get to above 40 you will see no solo quests. So level up slowly.

    In esteldin a lot of people ask for fellowships on quests that are solo able, granted you at the very least on the level of the quest. It just takes a lot of cunning and patience.
Also, even though the game isn't as populated as some other games out there, for most quests you can find groups easily enough. There are always people leveling alts in those regions.

    Still plenty of Solo quests left to get players to about 34-35ish all over the world.
Also grinding is always an option and rested xp bonus comes fairly quickly if you level other toons in the meantime (I have a guardian alt I'm working on as well).
40+ is where a large part of the player base is so you don’t need to worry about finding a group.

    Despite what some people say, you can find solo content all the way to level 50. When you need to do a fellowship quest, put it on the back burner and keep your eyes open on the LFF channel. You do not want to level up in one starting zone. Make sure you do quests in Erud Luin, The Shire, and Combe/Bree and get started on deeds in these areas while the xp earned is beneficial. You earn traits for completing a certain number of quests in each area.

    Also do not be too quick to jump to higher level zones if you are mainly solo. It is much easier to fight blue mobs than yellow, especially if you need to defeat 2 or more at once (with no help). Your champion should serve you well with this.

    As far as the level range that contains the most players, Turbine gives out no figures and don’t know whether there is a valid source for your information. Just because you claim it's a fact don't make it so!

    None of the 50s has any trouble finding groups what so ever. To the OP - play at odd hours & enjoy soloing and yes, you should be able to make it to 50 without ever needing a group. You won't see the heroic content - the raid zones and some of the tougher instances but unless you're the "I have to see EVERYTHING" kind of player, that won't detract very much from your gaming experience. So dig in and enjoy!

    You can mostly solo the Tal Bruinen content starting at level 40. You may be needing help killing the trolls for one quest and the wolfmen for another. Gollem encounter IS solo only.
For a captain who is level 44:

    Levels 35-40 Evendim. Mostly Solo. Help with Wolfmen and Giant quests (one other person).  Tomb of Elendil and Theif-taker's Bane are the notable fellowship quests that need a FULL fellowship. I have only done these on 2 of 5 characters.
40-45 Misty Mountains, Aughaire, Tal Bruinen, Gerbiltown (East Angmar). Many quests were given in Rivendell, the run up to Misty and Gloin's camp. Some are just go look and report back (survive hehe). Earth Kin camp in Angmar and the Hillman camp, many are soloable and many fellowship quests need only 2 or 3 and everyone is doing those.

For other level 50 characters:

    45+ High Pass of MM. Goblin Town you need at least 2 or 3 but lots of the chains are solo-able to start. East Angmar--GF/Himbar, many are soloable but hairy; you need to be real patient. 47+ in Himbar since many mobs are level 49-50. Your level 45 class quests can be done mostly solo until you get to the end and need parts from CD and Uru. But these parts are also tradable sometimes decent price sometimes not.
Whine all you want about no solo content past 40. You have to be patient and willing to try things.

    Some classes lend well to soloing past 40. You may end up doing blue or light blue quests but the 1-2K xp adds up.

    Seriously, if you had to, you could solo 1-50, it would not be easy but it is not impossible or even impossibly hard.