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ktreyb
The second step is wrong. 

To find the factors so you can set up two binomials in a polynomial set up in the format Ax² + Bx + C, you must find out what 2 factors of A * C would add up to equal B.

In this case, we have to find what factors would multiply to become - 6 but add up to be 1. Our factors are - 2 and 3 (3 - 2 = 1, 3 * - 2 = - 6). Step 2 in the expression above includes the opposite. 
jcherry99
It's right in the second step you've written.
3(2x^2 + 3x - 2x + 3) Is the right way to get the middle term to x.
3( (2x^2 - 2x) - (3x - 3) )  Factor out the first set of brackets
3((2x(x - 1) - 3(x - 1) )
3((x - 1)(2x - 3))