Simplify the circuit first if possible, like look at R5 and R6 and think about ways to simplify the combination of them that won't affect the voltages that you are trying to calculate.
Then just write a set of simultaneous equations that express how the currents flow through the different legs of the circuit, and solve for the two node voltages marked in red. Like, label the circuit with I1 going from the + (right) of the power supply, through the leg with R3, R4, R1. Label I2 as the current through the circuit leg through R2, R(combo), R7, R1. Then write equations for each node in the circuit, with the sum of all currents entering a node = 0. Solve away...