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enter image description hereI would like to solve it for P when Q=0. I know it can be done by "FindRoot/Reduce" commands. But for that, I would have to assign numerical values to all the characters except P. I don't want that. How can I solve it for P without assigning any numerical values to other characters? Can anyone help? For convenience, I have attached a snapshot of the equation.

Q=(((G+k μ-P)^2+4 k (G μ-μ P+1)) sinh((L Sqrt[(Sqrt[(G+k μ-P)^2+4 k (G μ-μ P+1)]-G-k μ+P)/(G μ-μ P+1)])/Sqrt[2]) sinh((L Sqrt[-((Sqrt[(G+k μ-P)^2+4 k (G μ-μ P+1)]+G+k μ-P)/(G μ-μ P+1))])/Sqrt[2]))/(G μ-μ P+1)^2

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  • 1
    $\begingroup$ Look at Solve. However, your equation is quite complicated, I do not think it can do what you want. $\endgroup$
    – yarchik
    Mar 21, 2021 at 15:52
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    $\begingroup$ Note that your function in a product of three terms. The product is zero when any of the three are zero, so you can reduce this to three separate smaller problems. $\endgroup$
    – bill s
    Mar 21, 2021 at 16:34

1 Answer 1

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Clear["Global`*"]

After correcting the syntax errors and using the approach suggested by bill s

Q = (((G + k μ - P)^2 + 
       4 k (G μ - μ P + 
          1)) Sinh[(L Sqrt[(Sqrt[(G + k μ - P)^2 + 
               4 k (G μ - μ P + 1)] - G - k μ + 
             P)/(G μ - μ P + 1)])/
       Sqrt[2]] Sinh[(L Sqrt[-((Sqrt[(G + k μ - P)^2 + 
                 4 k (G μ - μ P + 1)] + G + k μ - 
               P)/(G μ - μ P + 1))])/Sqrt[2]])/(G μ - μ P + 
      1)^2;

sol = Solve[#, P] & /@ Thread[(List @@ Q) == 0] // Quiet

(* {{}, {{P -> G + 3 k μ - 2 Sqrt[-k + 2 k^2 μ^2]}, {P -> 
    G + 3 k μ + 2 Sqrt[-k + 2 k^2 μ^2]}}, {}, {}} *)

Verifying,

Q /. sol[[2]] // Simplify

(* {0, 0} *)
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