Factor the four term polynomial by grouping 2x^2-8xy-9x+36y

2x^2-8xy-9x+36y=0
2x(x-4y)-9(x-4y)=0
(2x-9)(x-4y)=0

Factor the polynomial by grouping:

2x² – 8xy – 9x + 36y

Take out the greatest common factor of each pair of terms. For instance,

•  the greatest common factor of  2x²  and  – 8xy  is  2x,  so rewrite those terms as a multiple of  2x:
 
   2x² = 2x · x       ✔

   – 8xy = 2x · (– 4y)          ✔

•  the greatest common factor of  – 9x  and  36y  is  9,  so rewrite those terms as a multiple of  9:

   – 9x = 9 · (– x)

   36y = 9 · 4y

Instead of factoring out 9, see what happens if you factor out  – 9:

   – 9x = – 9 · x       ✔

   36y = – 9 · (– 4y)          ✔

That last option is better for what comes next, which is factoring that polynomial by grouping.

Take the polynomial and rewrite it conveniently:

2x² – 8xy – 9x + 36y

= 2x · x + 2x · (– 4y) – 9 · x – 9 · (– 4y)

Just take out common factors.  From the first two terms,  take  2x  out, and for the last two, take out  – 9:

= 2x · (x – 4y) – 9 · (x – 4y)

Now, (x – 4y) is a common factor, then just take it out to finally get to the factored form:

= (x – 4y) · (2x – 9)   <———   this is the answer.

I hope this helps. =)

The answer is