Combine like terms in Qx + 12 = 13x + P:
x(Q-13) = P-12
P-12
Then x = ----------
Q-13
Note that Q may not = 13. But none of the answer choices present Q = 13.
Let's go thru the answer choices one by one.
P-12
x = ----------
Q-13
-24
Check out A: Q=12 and P= -12: x = -------- = 24 This is OK (ONE sol'n)
-1
-25
Check out B: Q = -13 and P = -13: x = ----------- = 25/26 OK
-26
13-12
Check out C: Q = -13 and P = 13: x = ------------ = -1/26 OK
-13-13
12-12
Check out D: Q = 12 and P = 12: x= ---------- = 0 OK
12-13
It appears that in all four cases, the equation has ONE solution.