Hi,
6x^2 + 7x = 3
6x^2 + 7x - 3 = 0 |Subtracting 3 from both sides of the EQ
(3x -1)(2x +3)= 0 | Note:SUM of the outside terms(9x) and the inside terms(-2x) = 7x
The Idea is to match Up the -1 and 3 with the 2 & 3 so one gets that 7x
Checking the factoring Using FOIL
F First terms
O Outside terms 9x
I Inside terms -2x
L Last terms -3