Analyzing circuit with dependent sources
First, see that in the upper wire you have $$I_1=-2 Vx$$ and you can write:
$$I_1 = I_2 + I_3$$, where I_2 is the current in the 2nd wire (from left to right) and I_3 is the current in the other one.
Now, you have to "decide" where the Ground is and just solve equations.

Note that V_Z has the same  voltage that the - of V_x. Using that, I got:
$$I_2 = -\frac{V_Z + V_X}{R_2}$$
$$I_3 = \frac{15V - V_Z}{R_3}$$

If you don't know V_X, you can have it using that $$2V_X = I_2 + I_3$$