Linear Circuit Analysis: Source Transformation of DC Network
I neglected the middle resistor in bridge circuit,


um, you can't do that! it's plain wrong. I don't know how you came to the conclusion you could do that.

In fact, this is like the last transform I'd do. Start with resistors that are directly without doubt and branches serial, or parallel. 


  resistor in parallel with voltage source


there's more than that single transistor!