factor: 6x^2-7x-3 I am confused?

6x² - 7x - 3 = 0
x² - 7/6x = 1/2
x² - 7/12x = 1/2 + (7/12)²
x² - 7/12x = 72/144 + 49/144
(x - 7/12)² = 121/144
x - 7/12 = ± 11/12

= x - 7/12 - 11/12, = x - 18/12, = x - 3/2, = 2x - 3
= x - 7/12 + 11/12, = x + 4/12, = x + 1/3, = 3x + 1

Answer: (2x - 3)(3x + 1) are the factors.

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

6x^2 - 7x - 3
= 6x^2 + 2x - 9x - 3
= (6x^2 + 2x) - (9x + 3)
= 2x(3x + 1) - 3(3x + 1)
= (3x + 1)(2x - 3)

6x^2-7x-3
=6x^2+2x-9x-3
=2x(3x+1)-3(3x+1)
=(2x-3)(3x+!)