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MotherRhea
The way I usually solve these problems is by using trial and error. A good way to find out about where your numbers are is by finding the square root of that number. The square root of 306 is about 17.5, so I would start with 16 and 17. 17*16=272, so I would know I had to go higher. I would then try 17*18 which equals 306. Because you need the numbers to be negative, you would make both of those numbers negative. The two integers would then be -17 and -18.
18 and 17.  To solve this it helps to try numbers that when they multiply together will get a units digit that you need, for example, 8*7=56, and 6 is the last number needed, and 8*7 is too small, so try 18*17.  There is a chance one would have tried numbers ending in 2 and 3 but none work.

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