factoring by grouping

Any help with this problem:

7a - 35 - a^2 + 5a

Here is what i have done:

7a - 35 ; - a^2 + 5
I grouped them up there. I figured the GCF was 5.

7a(a-5) - a^2 (a - 5)

This is where I got stuck
My book says the answer should be (a-5) (7-a)
I am not sure how to get there from here.
Thanks so much. :D

[soroban]

Hello, afreemanny!

You're almost there . . . (despite a tiny error).


7a - 35 - a² + 5a

Here is what i have done:

7a - 35 ; - a² + 5

I grouped them up there. .

7(a - 5) - a(a - 5) . . . . Good!

This is where I got stuck . . .
Do you see what you have? . . 7(a - 5) - a(a - 5)

You have two terms with a common factor . . . take it out: . . (a - 5) (7 - a)


. . You "take it out" just like you "took out the 7" and "took out the -a" earlier.

I really shouldn't do this crap when I am tired. I am 38 with three kids, a full time job and going to college.....what is wrong with me??? :) I do appreciate all your help and love this site.

[tkhunny]

We do try to be beneficial. Just keep showing your work and we'll be even beter at it.

Hang in there.