Question

Divide 51 into two parts such that their product is 378

Answer 1

Let part one be x 
so part two will be 51-x
x into (51-x) = 378 
51x - x² = 378 
-x² + 51x - 378 = 0 
factorising it, we get
-x² + 42x + 9x - 378 = 0 
-x (x - 42) + 9 (x - 42) = 0
(-x+9) (x-42) = 0 
so x = 9 and x = 42 are the two parts