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I'm having a hard time looking for the distance ($x$) on which the forces must be located for a maximum bending moment. The reaction forces in $A$ and $B$ are dependant of the value of $x$, and so changes both the shear stress and the bending moment and I don't know what to do.
P, d and L are known constants.
The max bending moment occurs at the point at whcih the shear force is 0, therefore, you need find an expression for the shear force acting on the beam taking the two forces 2P and P in consideration. Once you have found an expression for the shear force (it should be a function of x), then you could either analyse the beam again and find the expression of the bending moment, or you could set the derivative of the shear force with respect to the distance x to 0 and solve for x.
Hope this helps!
