The above fact works only if the leading coefficient is 1. That is you must have an equation of the form . But don't worry. You can do that just by dividing the 6 out. You get
from here and
based on this text:
How to Factorise a Quadratic Expression | eHow.com
You factorise the quadratic expression x²+ (a+b) x +ab by rewriting it as the product of two binomials (x+a) X (x+b). By letting (a+b)=c and (ab)=d, you can recognize the familiar form of the quadratic equation x²+ cx+d. Factoring is the process of reverse multiplication and is the simplest way to solve quadratic equations.
But I found an equation which has solutions and is not congruent with the above text, like:
Since the solution is: (2x-1)(3x+4)
Based on the above text means, (a*b)=d --> (-1*4)= -4 ok but;
(a+b)=c --> (-1+4)= 3 is not ok sine in the equation is 5.
Please help me out... how this is possible etc.