Implicit Differentiation Problem

I've been stuck on this one for quite awhile now.

Find the slope of the tangent line to the curve

https://webwork.math.ohio-state.edu/...c7c70e06a1.png

at the point (3, 7).

I basically understand implicit differentiation for the most part, I believe I am just stuck on the arithmetic. I can't get y' (dy/dx) to one side.

I rewrote the equation:

(x+2y)^(1/2) + (2xy)^(1/2) = 10.6

I then used the chain rule on both terms:

(1/2)(x+2y)^(-1/2)*(1+2y') + 1/2(2xy)^(-1/2)*(2xy'+2y) = 0

Then I simplified equation by moving ^(-1/2) to denominator:

[(1+2y')/(2sqrt(x+2y))] + (2xy'+2y)/(2sqrt(2xy)) = 0

And them from here I cannot understand the arithmetic to solving for y'. Any help would be appreciated, again, I'm pretty sure I'm correct to this point, I just don't know how to get y' by itself.