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nsmet error in a simple equation which I can solve by hand

Dear Mathematica users,

if I enter the following command in Mathematica:

E^(-r t) (-E^(r t) + (L + s)^-\[Alpha] ((L + s)^(1 - \[Alpha]) + (1 -
c) t)^(-1 + 1/(1 - \[Alpha]))) == 0
I get this error: Solve::nsmet: This system cannot be solved with the
methods available to Solve.

All I want to do is rewrite the equation on terms of L. The thing is
that it easily solvable by hand by factoring out, having E^(r t) on
the RHS and then raising each side by (1-alpha)/alpha.

Do you have an idea how to solve this problem? Thank you for your

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