I need help with this. I have pretty much no clue where to start. It's should be a simple "Find V" problem but it's not . . .

 

Find voltage across 15 kOhm, V15.
Find voltage across 12 kOhm, V12.
V0=V15-V12

 

It's should be a simple "Find V" problem but it's not . . .

You're right it is more complicated than that. You have to find two voltages then sum them.
What sort of training have you had in solving simple resistive circuits? Any?
Are you familiar with Kirchhoff's laws?
Give us a clue what you have done to attempt to solve it.

 

I ended up just getting a solutions manual since I realized it'll be a long semester . . . and unless I make it click my way, it never will.

So it solved each branch first. I understand that, using the parallel knowledge (and that's circuit division, yes?). IE [(10+15)//(3+12)]/(10+15) * 18

The left most was 6.75 mA, and the right most 11.25 mA

Then they calculated voltage across each resistor towards the top, which I also understand. IE V15 = -(6.75)(15) because of the direction of the current source.

The final equation they got was V = -101.25- -135. I understand everything up until the end . . . Wouldn't that entire "lower wire" (is node appropriate?) be one voltage? Why the subtraction?

 

It often helps to label the diagram very explicitly and work from what you want to what you know.


(Q1) In terms of the node voltages (marked in green) what is the expression for the vo in terms of Va and Vb?

(Q2) What do you know about the current I3 and I4?

(Q3) As a consequence of (Q2), can you write vo in terms of Vc and Vd?

(Q4) Can you determine I1 and I2 given the results of (Q2)? You've already done this, but do you realize that the method you used is ONLY valid as a result of the answer to (Q2)?

(Q5) Can you find Vc in terms of Vf and I1?

(Q6) Can you find Vd in terms of Vf and I2?

(Q7) What happens when you combine the results of Q5 and Q6 with Q3?

At this point, you should realize the it doesn't matter what the voltage of Vf is.