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:

6x^2+5x-4=0

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.