I presume you want to find d in this situation.
If we start with 4d+1/d+9=-3/-2 we an see this is the same as 4d+1/d+9=3/2 as the negative number cancel to make a positive fraction.
Then we can multiply both sides by d+9 to get:
4d+1=3(d+9)/2
We can now multiply both sides by 2 to get:
2(4d+1)=3(d+9)
Now expand to get:
8d+2=3d+27
And now take away 3d from both sides to get:
5d+2=27
And now take 2 away from both sides to get:
5d=25
Finally divide both sides by 5 to get:
d=5