3 x 3 Mixed Strategy Nash Equilibrium

Question

                                                    Column
                                           Left         Middle          Right
       
            
                                 Up        2,10         1,  3           7, -4                                                
                         Row   Sideways    7, 6        −7, −16           2, 5                         
                                Down       6, 1          2, 20          0, 15               

I'm having trouble finding the mixed strategy equilibrium for this game

I've already concluded there is no iterated dominance and have found two pure nash eqilibria (S,L) and (D,M) Now I need to find the mix strategy nash equilibrium but I've gotten 3/5 probability for p2 R and 1/5 for the remaining but they don't make sense when I plug them back into the formula.

Answer 1

Conjecture that player 1 plays Up with probability $p_1$, Sideways with probability $p_2$ and Down with $1-p_1-p_2$. Do the same with player 2. If player 1 is playing a mixed strategy then the expected payoff of playing either Up, Down or Sideways must be equal. Use that to solve for $q_1$ and $q_2$. Repeat for player 2 to solve for $p_1$ and $p_2$.