Answer:
-18, -12, 0, 25, 5
0, -12, 5, -18, 25
25, 0, -18, 5, -12
-12, 25, 5, 0, -18
5, -18, 25, -12, 0
Explanation:
The only values you need to use here are 0, 5, 25, -12, and -18.
I started with the bottom right box because the far right column only had one empty box. From the set of values I stated above, that column already had each of those numbers except for 0, so 0 would go in the bottom right box.
Another way to think about it is each row or column must have a 5 and a 25 to make 30, and a -12 and a -18 to make -30. Those two numbers cancel each other out to make 0, and then each row/column will include a 0 value which obviously wouldn't effect that balance. So the whole row/column will come out to be 0.
After figuring out that first bottom right box, go to the next row/column with only one empty box left (this happened to be the very bottom row), and use the same strategy to fill in the missing value.
Continue finding the next row/column with only one empty box left and figure out its missing value until you've completed the whole box.