First, you need to factor the polynomial.
I'll use the trial and error method.
6x^2 - 5x - 6 = 0
6 has factors
6 and 1
3 and 2
I'll try 3 and 2 first.
(3x )(2x ) = 0
Now we need to factor -6.
-6 factors into
-1, 6
-6, 1
-2, 3
-3, 2
Now we need to see if one of these pairs of factors placed correclty will factor the trinomial.
(3x + 2)(2x - 3) = 0
That did it.
Now we use the zero factor property.
3x + 2 = 0 or 2x - 3 = 0
3x = -2 or 2x = 3
x = -2/3 or x = 3/2
