Which values of P and Q result in an equation with exactly one solution?

Qx+12=13x+P

a. Q=12 and P=-12

b. Q=-13 and P=13

c. Q=12 and P=12

d. Q=-13 and P=-13

Another question for my impossible math question file.

All of the given pairs of values result in an equation with exactly one solution, as will any pair such that Q≠13 and P≠12.

For Q=13 and P≠12, there is no solution.

For Q=13 and P=12, there will be an infinite number of solutions.