Why does my voltage (reduced with a voltage divider) drop to zero when connected to a 6V DC motor?
See that 1k resistor?  At 6V, you can get about 6 milliamperes of current through it.
Your motor needs far more than 6 milliamperes of current to run.  Your motor looks like a short circuit when compared to that 1k resistor.  The voltage drop across the motor will be very small - almost all of the voltage drops across the resistor.
Remove the resistors, and don't sweat that 1 volt difference between the power supply output and the motor rating.  The motor will run a little bit faster, but it shouldn't bother anything.