# Thread: isolating and solving for a variable

1. ## isolating and solving for a variable

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.

2. Originally Posted by Wowbagger
(sin80/sin10)*T*cos10 - T*cos80 - W = 0
Isolate the W:
(sin80/sin10)*T*cos10 - T*cos80 = W

Now notice that the LHS has a common T. Factor this T:
[ (sin80/sin10)*cos10 - cos80 ]*T = W

Now, (sin80/sin10)*cos10 - cos80 is just a number. Divide both sides by it:
T = W/[ (sin80/sin10)*cos10 - cos80 ]

-Dan

3. Very cool, thanks so much.