Engineering Op-Amp Resistive Circuit Homework: Finding Vo in a Given Circuit

[sojo]

Homework Statement

The attached picture is the circuit I have been given and I am asked to find Vo (the voltage drop across the 6k resistor.

Homework Equations

v_out/v_in = (R_1 + R_2)/R_1
V+ = V-

The Attempt at a Solution

So I know that the voltage drop across the 6k resistor is just the output voltage of the op-amp since there is a ground there.
I used the v_out/v_in = 3+9/3 = 4, so I know V_out = 4V_in
The thing I am having issues with is finding the V_in. I feel like I have 7 unknown currents and I've written out a ton of equations using the KVL and KCL but I feel like I just keep running around in circles with all the unknowns.
Am I going to have to use all the KVL KCL equations to solve this, or is there some simpler method I am missing to find the Vin so I can find the Vout?

 

[NascentOxygen]

v_out/v_in = (R_1 + R_2)/R_1
V+ = V-

You used "conservation of current" to establish V– in terms of Vout. So now you use that same "conservation of current" law to find V+ in terms of Vout and the 4V. The current into the resistor network equals the current that flows from the resistor network.

 

[LvW]

Just a hint: All you need is the positive feedback factor k+ (setting the 4V dc source equal to zero).
In this case, we have Rp=4k||5k=2.222k and the problem reduces to two simple resistive voltage divider in series.
This shouldn`t be a big problem.