Is there a mistake with this national income model Mik. Wisniewski Intro to Math Methods in Econ pg. 61

Question

I can't figure out the steps to this equation for the national income model.

It seems simple, but I don't see why in step 4 I don't get Y-bY+tY

I thought it was a mistake in the book at first, but that would make the whole model wrong, so is there something I am missing?

Y = C+I+G
Y = a+b(Y-tY)+I+G
Y-b(Y-tY)= a+I+G 
Y-bY-btY = a+I+G  (I'm lost here, why isn't it Y-bY+btY?)

Y(1-b-bt) = a+I+G
Y(1-b(1-t)) = a+I+G
Ye = a+I+G / 1-b(1-t)

Thanks for the help!

Answer 1

There is a mistake in the book at step 4, and the income equilibrium equation is correct.