How do I calculate the reactant forces for the supports of the beam where the centre of mass is not same distance from each support?

This can be done by taking moments. To reduce the number of equations a moment should  be taken so that one of the forces goes through the centre of place from which moments are being taken. We will choose to do this at one of the supports. Define anti-clockwise moments as postive and work out all the moments about this point by multiplying the force by the distance away from the point at which we are taking moments. As there is no overall acceleration, the sum of the moments must equal zero. This equation can be solved to find one of the reaction forces. The sum of the reaction forces must equal the weight of the beam. Using this the reaction force on the other side of the beam can be found.