Find all solutions to:
ab + 2a + 2b = −16
ac + 2a + 2c = 26
bc + 2b + 2c = −44
+289 Using Simon's Favorite Factoring Trick to all of the equations gives us:
(a + 2)(b + 2) = - 12
(a + 2)(c + 2) = 30
(b + 2)(c + 2) = -40
Multiply all those equations together gives us
(a+2)(b + 2)(c + 2) = 120
Applying these into the equations gives us:
-12(c + 2) = 120
30(b + 2) = 120
-40(a + 2) = 120
c = - 12
b = 2
a = -5
