please tell me some tricks about middle term splitting

eplaining with an example:-

see,if following is the question,

2x²-5x-3, then,

you'll multiply the last no. with the first no.,

=2 * 3

the ans.come 6.

the you'll take all factors of 6 and see that which one is the factor whose sum or difference would be equal to the middle term(5)

=factors of 6

=2 * 3, 6 * 1.

here we see that the second factors i.e. 6 and 1 are the no. whose difference comes 5.

=2x² + 1 x - 6x - 3

=x(2x+1) - 3(2x+1)

(x-3) (2x+1) will be the ans.