What are integer values for c in the following:

2 x^2 + 5 x + c = 0

What's the logic/method to get c with using a calculator, Excel,... I don't see how to uss outer/inner combo or AC grouping.

c can have an infinite number of values.

2x^2+5x+c can be
(2x+1)(x+2) if c = 2
(2x-1)(x+3) if c = -3
and many more.