Having trouble finding Vo, V1 and V2 in this circuit (not homework)

circuit analysis

I'm working out textbook examples to get better at beginner analysis. I'm having trouble with this circuit.

schematic

simulate this circuit – Schematic created using CircuitLab

Steps I've tried:

1) 10k*20k / 30k = 6.6666...k ohms
2) 5k*10k / 15k = 3.3333...k ohms
3) those are now in series, for 10k ohms equiv on the left side
4) from the right, 8k+4k = 12k ohms
5) 144k / 24k = 6k ohms
6) 6k + 4k = 10k ohms equiv. on the right side
7) now the 3k ohm resistor is in parallel with both the 10k ohm equiv resistors
   on both side, so I know the voltage across both 10k ohm resistors is 16V.  
   Calculating current, I find that current is 1.6mA across each combined 10k 
   ohm resistor
8) now, splitting the 10k ohm resistor into the 6k and 4k in series, i know they
   both share 1.6mA current; thus V1 = 1.6mA * 4000 ohms = 6.4 V.

I stopped here because I got the wrong answer. Will someone please help me figure this out?

Best Answer

After step 6, your circuit will be as shown below.

schematic

simulate this circuit – Schematic created using CircuitLab

Which can be further reduced as a 16V battery in series with 3k and 5k resistors.

Now, you will have 10V across this 5k resistance, ie, 10V across each parallel 10k. Splitting 10k into 6k+4k, you will have 4V across 4k resistance. From the polarity of v1 marked, V1= -4V.

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