<s>[INST] How do you factor this equation that has square roots involved? I'm trying to solve this equation for 
$$\sqrt {16+l^2} + \sqrt {4+l^2} = {nv \over f}$$ 
I know what ${nv \over f}$ is, but no matter what I do I keep getting a weird answer. I've resulted to using Wolfram Alpha, but I'd really like to know how to do this myself. 
 [/INST] Square-rearrange-square again as garserdt216 outlined totally works. I'm not going to solve your problem but here see it applied to an equivalent generalized problem
$$\sqrt{x + a} + \sqrt{x + b} = c$$
Square
$$(x + a) + 2\sqrt{(x + a)(x + b)}+ (x + b) = c^2$$
Isolate square root
$$\sqrt{(x + a)(x + b)} = \frac{c^2 - a - b}{2} - x$$
Square again
$$(x + a)(x + b) = \left (\frac{c^2 - a - b}{2} - x \right )^2$$
Simplify
$$x^2 + (a + b)x + ab = x^2  + (a + b - c^2)x+ \left (\frac{c^2 - a - b}{2}\right)^2 $$
Simplify some more
$$x = \frac{1}{c^2}\left ( \left (\frac{c^2 - a - b}{2}\right)^2 - ab \right ) = \frac{(c^2 - a - b)^2 - 4ab}{4c^2}$$
(Check for consistency with original equation.)
EDIT: Thanks to @Claude Leibovici for pointing out some errors which I've now hopefully corrected. 
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