I am trying to get an understanding of how these expressions are understood.

I have an example that I am working on which I require to use Identities to find a value of X.

The closest example that I can find at the moment from books is this Nested Brackets example;

7(a - {4 - 5(b - 3a)}) = 7(a - {4 - 5b + 15a})

= 7(a - 4 + 5b - 15a)

= 7a - 28 + 35b - 105a

= 35b - 98a - 28

So in the above example if I had to work that out starting from the top left hand side, I would follow through as;

-5b then -5 x -3a = + 15a, so at this point I now have;

-5b + 15a

then I would say 7 x a = 7a, and then 7 x 4 = 28, therefore;

then 7 x 5 = 35b, then 7 x (-15a) = -105a

so;

7a - 28 + 35b - 105a = 35b - 98a - 28

The part I don't understand?

How does -5b become +5b, and how does +15a become -15a?

I don't understand it?