What you have done is called factorising. By putting it into brackets you have factorised the equation.
On the whole, factorising (in mathematics) is a good thing and will usually help you arrive at a solution to a problem. It is a bit of a mantra in my A-level classroom: “factorise first”
You are very kind mentioning A-Level classes. You know as well as I do that my brain block today was very much GCSE level.
Rather ironically, I took my GCSE's a year early, did AS level statistics in the 5th year (11) and then did A-Level Physics. I'm not a complete moron when it comes to numbers, but as I said in the OP, I just confused myself.
I'll give the equation some context so you can see just how basic my confusion was.
I'm doing some work for a client for 30 % of the total income, minus some expenses we will encounter. We were talking it over on the phone and he mentioned that we should decide if we take the costs off of the total before or after we do the split 30/70. I said it would make no difference, I'll end up paying for 30 % of those costs regardless, he disagreed initially but then once he thought about it wasn't sure. As we had other matters to discuss we just carried on with the conversation, both (I think) trying to get our heads around the maths issue in our minds, and both failing miserably.
I think if I sat and thought about it I'd have understood it immediately, but after mulling it over with my mind on other things, my poor brain didn't know which way was up.
I then decided to put the calcs into equations, because then it would be obvious. The equations are based on the following.
T = Total income.
C = Costs.
H = My share
As you can see. The equations are for two options. The first, I get 30 % minus 30% of the costs, and second we take the costs from the total and I get 30 % of whats left.
Anyway, I thought anyone who's vaguely interested may also be interested how incredibly basic the cause of my confusion was.
On the bright side, UKBF reassured me in a matter of minutes. Thanks again
@KM-Tiger
