Hi grapeman,
Your work is right since it was assumed that the transistor is linear (given beta=Ic/Ib=300). But if we find out that the result cannot be real then this leads us to think that something we have assumed wasn't a good choice in the first place (hence it wasn't your fault).
In this special case (circuit), we consider the transistor being saturated. In other words, Vce (or Vsat) is close to zero (about 50 to 400 mV and this depends on Ic/Ib. For instance, decreasing Ic/Ib decreases Vce but at a much slower rate).
The new equations would be:
Vcc - Vsat = Ic*Rc + Ie*Re
Ie = Ic + Ib
Note: Here Ib is not negligible
Vb= Vbe + Ie*Re
Ib = (Vcc - Vb)/Rb1 - Vb/Rb2
Unkown: Ic, Ib, Ie and Vb
Known: Vcc, Vsat, Rc, Re, Vbe, Rb1 and Rb2
And we have 4 equations
Good luck.
Kerim
Added:
Obviously this circuit, as it is, doesn't work as it was supposed to do... as an AC amplifer.