What is your question? If you just need an expanded solution to this, then this would be the process.

In order to get the square of a binomial, you have to:
1. Get the square of the first term, then add it to...
2. Two times the first term and the second term. (The sign depends on the terms)
3. Lastly, add the square of the second term.

With your equation, we get:
(x+4)^2 + (y-5)^2 =36

=>(x^2 + 8x +16) + (y^2 -10y + 25) =36

Combing like terms,
=>x^2 + y^2 +8x -10y + 41 =36

=>x^2 + y^2 +8x -10y +5 =0

I hope that answers it. 
By the way, this is an equation of a circle with radius 6, with its center at (-4, 5).
Message me if anyone wants to know the details for that. ('Cause it will take another typing session which, well, takes time. lol)