General rule of thumb: Ending in LL is generally a very bad idea for FMC. Use of blockbuilding, influencing future steps, and commutators/conjugates are the most important things to have in your toolbox for FMC. What most top FMC solvers do is a Petrus style solve; usually doing 2x2x2->2x2x3+EO and building F2L while solving to an LxC state (which usually is L3/4C including an F2L corner.) Here's my attempt with this scramble (21 moves):
B' L' B U//2x2x2
z2 U' R2 F2 R F' R F'//EO2x2x3
U2 R2 U D' R U R' D R' U//L3C redux
Notice how I utilized premade pairs to make the rest of the solve more efficient, especially during EO. I saw the pair in DRB and knew I needed to preserve it to make L3C very simple. I utilize it during LxC redux to make it very efficient. Also, notice how I didn't restrict myself to just <RU> while doing F2L->L3C redux. By incorporating other moves, you can solve all the edges much more efficiently. While there were two 4 move 2x2x2's and I tested all their directions, this was the most efficient one that I saw, so I used it.
At this point, the cube can be solved using a simple 9 move commutator (29 moves):
B' L' B U//2x2x2
z2 U' R2 F2 R F' R F'//EO2x2x3
U2 R2 U D' R U R' D R'//L3C redux
U' B' D B U' B' D' B U'//L3C
However, when we do a "true" FMC solve, it is generally done without any rotations, hence why this final solution will be slightly different. We will use what is known as an "insertion" to solve the corners early in the solve, which can save several moves. This is a very important technique that I can't explain very well, so I'd recommend looking it up on the Forums or a YT search. Anyway, here's the end solution (27):
B' L' B U D' [#] L2 F2 L F' L F' D2 L2 D U' L D L' U L' D
#: D2 L' U' L D2 L' U L
B' L' B U
D' [D2 L' U' L D2 L' U
L] L2 F2 L F' D2 L2 D U' L D L' U L' D
B' L' B U D L' U' L D2 L' U L' F2 L F' L F' D2 L2 D U' L D L' U L' D
Good solution for me, feel like it had a lot of good techniques for beginning FMC solvers.
I know this isn't massively helpful, but I urge you to continue with FMC, it's a really fun event IMO. GO to the FMC thread here on the forums, watch tutorials, read on techniques, etc. No shortage of material on FMC. I reccomend going on the weekly FMC challenge website to see tons of good example solves as well. Hope this helped in some way to the basics anyway!
Oh and Roux, 38
y R F' U' L' D2 F//FB
U R' U r2 U M U' R2 U2 R//SB
U' R U R' U R' F R F' R U2 R'//CMLL
M U2 M U M2 U M2 U2 M' U'//LSE
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