Factoring, Algebra question. Please help.?

Question

This isn't homework or anything, I'm just having trouble understanding how factoring works. Could you please factor the following completely, and explain your work?

12a^2(x-7)-75(x-7)

Thanks in advance.

Answer 1

ab - ac = a(b - c)

I see a common (x - 7) term and a 3 (from 12 and 75). Take those out!

3(x - 7)(4a² - 25)

4a² - 25 can factor again. It's a difference of perfect squares...

3(x - 7)(2a + 5)(2a - 5)

these just take practice, you'll get it

Answer 2

gather like terms

it should be

12a^2(x^2-7^2)-75