Hi, I'm currently trying to find the equation for a decision variable from a total profit equation using Mathematica. From what I've read, I can use the solve function to do this. Here's a example i found:

(*Define the total cost function*)
TC[Q_] := (D S/Q) + (H Q/2)

(*Compute the first derivative*)
dTCdQ = D[TC[Q], Q]

(*Solve for Q*)
solution = Solve[dTCdQ == 0, Q]

(*Simplify the solution*)
simplifiedSolution = Simplify[solution]

However, when I try to apply this to my actual equation, the program runs for hours without completing (it stuck). Here is my specific code:

TP[x_] = pr/x ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(1/(
   1 - b)) - ((c + 1) (Kr/x + Kp/(n x) + Kf/(
      n x) + (hr + g)/
       x (2 x (-((a (-1 + b) g x^2 y)/(L + g L y)))^(1/(1 - b))) + (
       hp + g)/(2 R x) ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(
       2/(1 - b)) + ((hp + g) (n - 1))/(
       2 x) ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(2/(
       1 - b)) (x ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(1/(
          1 - b)) - 1/R) + 
      1/x^2 S + (v/x + vp/(n x)) ((a (1 - b) (x^2))/(
         2 L) ((y g)/(1 + y g)))^(1/(1 - b)) + 
      1/(n x)^2 Sv + (Pv w)/( 
       x f ww) ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(1/(
       1 - b)) + (((cf f) + (m bk))/( 
        x f ww ) {k n x + 
          k/q (Log[1 + z E^(-q n x)] - Log[1 + z])}) )) + (c ((pp/x + 
        pf/x) ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(1/(
      1 - b)))) + (pr/x l (
     2 a g (x^2)
       y (((-((a (-1 + b) g x^2 y)/(L + g L y)))^(1/(1 - b)))^b) )/(
     L + g L y) - ((a (1 - b) (x^2))/(2 L) ((y g)/(1 + y g)))^(1/(
     1 - b)) (M - x))
(*Compute the first derivative*)
dTPdx = D[TP[x], x]

(*Solve for p*)
solution = Solve[dTPdx == 0, x]

(*Simplify the solution*)
simplifiedSolution = Simplify[solution]

Any suggestions on how to resolve this issue? Are there more efficient methods or best practices I should consider for solving complex equations in Mathematica?