Inverting Op Amp question

There is an easier way to think about this problem, assuming ideal components. First, since the noninverting pin is grounded, the inverting pin is at virtual ground. This means:

\$V_{R1}=V_{in}\$.

\$\therefore I_{R1}=I_{R2\parallel R4}=I_{R3}\$

Calculate the voltage drop across \$R_{2\parallel 4}\$ in series with \$R_3\$, and you'll arrive at \$V_o\$ from there.

FWIW, here's another method; form the Thevenin equivalent circuit looking into R2 from the inverting input.

The equivalent circuit is, by inspection:

\$V_{TH} = V_{OUT}\dfrac{R_4}{R_3+R_4}\$

\$R_{TH} = R_2 + R_3||R_4\$

Now, there's just one node to consider. The KCL equation for the remaining node is, by inspection:

\$\dfrac{V_{IN}}{R_1} + \dfrac{V_{TH}}{R_{TH}} = 0\$