Question 442599
Here's the trick:

Take the a term and multiply it by the c term.  6 * -18 = -108.  List the factors of -108.

plus or minus
--------------
1  108
2  54
3  36
4  27
6  18
9  12

Is there any way to get -23 out of this?

yes, 4 - 27 gives us -23.

Thus we will have a 4x term and a -27x term.

so we can rewrite this as {{{6x^2 + 4x - 27x -18}}}

Group the first two terms and last two terms and factor out the common factor.

{{{2x(3x+2) - 9(3x+2)  = (2x-9)(3x+2)}}}

Thus our factorization is {{{(2x-9)(3x+2)}}}

Set each factor equal to 0:

(2x-9) = 0  ---> 2x = 9  x =9/2
(3x+2) = 0  ---> 3x = -2 x = -2/3

So our two solutions are {{{x=expr(9/2)}}}{{{x=expr(-2/3)}}}