After finding the total transformation matrix, we'll get three equations for the end-effector coordinates [dx dy dz]T. So how can we solve them for 4 (or 5) joints parameters in case of 4 ( or 5 ) dof robot manipulator?
First find TCV (Tool configuration vector) from the arm matrix of the given robot then compare TCV with the given position and orientation of the robot. On comparing you can easily find the values of join variables.
could you please make your question more clear so I can help you, do you have only position without orientation? it's important to know that both position and orientation will considerably affect on calculations of transformation and rotation matrices for any kinematic model.
I can suggest to watch lectures on youtube for salford university,
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