This is a basic algebra question set in a physics question. Yes I know I should have learned this a long time ago but I played cards through math class in middle school and it's finally catching up, thank you very much.

My question:

in my physics book they rearrange an equation from

this

(sin80/sin10)*T*cos10 - T*cos80 - W = 0

to

T = W / [(sin80/sin10)cos10 - cos80]

How?

I generally understand whats going on here, the W can be "added" to the other side and then divided by the various trig function however I don't know how I ended up with just one T on the left side. My instinct would be to try and combine them (2T or -2T?) but that's clearly not what happened.

suggestions? Thanks for your time.