Unable to solve equation for a variable by any method

I am looking to solve for the value of r when the derivative of the expression

 (1/ r^2) (1 - ((2*GM)/(c^2*r)) Integrate[t*Exp[(-t)], {t, 0, r/Sqrt[β]}]) 

equals zero.

But I have been unable to use the Solve, FindRoot, or Reduce to find a value for r. Mathmatica keeps returning

Solve::nsmet: This system cannot be solved with the methods available to Solve.

G, β, M, and c are all constants.

Please, any help would be much apreciated.