How Do You Solve This Complex Math Problem Step-by-Step?

[kuahji]

Can't figure out how the example in the book is getting from one step to the next.

Here's the problem
2(8+216/x)(-216/x^2) + 2(x+27) = 0

The next step
(x+27)(1-1728/x^3) = 0

First thing I did was divide out the two & got
(8+216/x)(-216/x^2) + (x+27) = 0
Then I multiplied out the left part
-1728x^-2 + 46656x^-3 + (x+27) = 0
This got me nowhere it seems.
Then I tried to find a common denominator
-1728x-46656/x + (x+27) = 0
this is what I got when I multiplied it out & still nowhere it seems. Any help would be appreciated.

 

[Integral]

Can't figure out how the example in the book is getting from one step to the next.

Here's the problem
2(8+216/x)(-216/x^2) + 2(x+27) = 0


The next step
(x+27)(1-1728/x^3) = 0

Nope. This is wrong, so all that follows is also wrong.

Next step:

\frac {- 8 (216)} {x^2} - \frac {216^2} {x^3} + (x+27) =0

now multiply through by x^3 to get:
-8(216)x - 216^2 + x^3 (x+27) = 0
now you should be able to continue.