I wasn't really sure where to put this problem, it is a college course but I'm having issues with the basic algebra. I figured this would be the best spot...
The textbook (macro econ) gives an equation and wants it in terms of Y, and gives the answer in two steps. I just cant figure out how the author did it.
Y=c0+c1*Y-c1*T+I+G
It then rearranges to
(1-c1)*Y=c0 +I+G-c1*T
Then it divides both sides by (1-c1) for
Y=1/(1-c1)*[c0+I+G-c1*T]
What I don't understand is where he gets the (1-c1) part. He obviously subtracted c1*Y from the right side and added it to the Y on the left hand side of the equation, but I don't know what identity he used to convert Y-c1*Y to (1-c1)*Y. Any help on clearing this up would be greatly appreciated. If any further clarification is necessary please let me know.
Thanks for your time!
Clarification: The c1 and c0 are c subscript 1 and c subscript 2 (not that it really makes a difference)