Let's analyse this from scratch for white.
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Analysis "Pros, Cons and Plans"
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White Pros: Active pices, Good amount of Atacking pices over blacks king, Rock behind an advanced pawn, "Iniciative", good comunication between pices.
White Cons: Behind material, Black side have a good bishop vs white un-posted knight.
Black Cons: Very misplaced pices especially the queen, bad comunication between pices.
White's Plan: Use the iniciative and active pices for an atack.
Black's Plan:Exange material specialy "queen's" if possible and head for an endgame keeping his edge on material.
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Design "Making it happen"
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We know that we want to atack, a basic tactic them when you are planing an atack its to "open lines" into enemy's king and actually 1.Rxe5 does that it open a line for our f pawn to avance further into enemys king position using the advantage that we already have a Rook behind it. lets say:
1. Rxe5 f6 2. Qg3 fxe5 3. f6 but this line gets refuted by 3... Qg4 4. Qxe5 Rf8 5.Qxd5+ Qe6 6.Qxe6 Bxe6 and this with carefull play from both players should be a draw.
Now we saw that retreting in the midle of the atack wasn't an option since it gave black chances to get his queen back to the defence of his king, so we need other tactic theme "removing/deflecting the defender" we need to take that queen away from the defense of the g4 square. we said in the pre requisits of the software... ehem i mean on the analysis part that the misplacement of the Blacks queen was a factor since she dont have to much place to move, also that our knight was not that useful at the moment so we can exchange some resources for others in this case material for time and quality. let's follow the next line.
1. Rxe5 f6 2. c3! Qxb3 3. Qg3 fxe5 4. f6 g6 5. f7+ Kg7 6. Qxe5+ Kh6 7.
Qf4+ Kh5
And his king its exposed if you ask me that worth more than an inactive knight now being on blacks shoes and knowing that taking that knight it isnt so much of a bright idea he can chose to play 2....Qc4 instead of 2...Qxb3.
3.Qg3 fxe5 4.Nd2!
We can't play f6 right away since it would open free the g4 square for black's queen.
4...Qe2 (trying to get closer to the defense) 5. f6 Qg4 (queen reach g4 but to late since we can move with tempo developing more atack over blacks king)6. Qxe5 Qe6 7. Qg5 g6 8. Nf3 Rf8 9. Ne5 Be8 10. Ng4 Kh8 11. h4
And the passed pawn and activity of white pices added to the iniciative should be winning.
So what if we play c3 first. it would go like this.
1. c3! Qxb3 2. Rxe5 f6 3. Qg3 Re8 4. Rxe8+ Bxe8 5. Qd6 Qxa4 6. Qxd5+ Bf7 7. Qd8+ Qe8 8. Qxe8+ Bxe8
This position its cleary wining for white too.
As conclution we can see that the key move its c3 to remove the queen from the defensive square g4 it doesnt matter if we play Rxe5 1st.
Anyway feel free to post any correction over my analysis.
c3 looks interesting
1. c3 Qxb3 2. Rxe5 f6 3. Qg3 fxe5 4. f6 g6 5. f7+ Kf8 6. Qxe5 Bf5 7. Qh8+ Kxf7 8. Qxa8
though not "winning" it leaves white ahead slightly. plus, if you can trade queens then you've got a king & rook v. king & bishop end game.