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I have \(\displaystyle \int \frac{x^2 - 5x + 16}{(2x + 1)(x - 2)^2} \, dx\)

and I got to this part:

\(\displaystyle x^2 - 5x + 16 = A(x - 2)^2 + B(x - 2)(x + \frac{1}{2}) + c(x + \frac{1}{2})\)

So do i need to distribute all of these and factor out or is there a simpler way? I found a solution where they are just saying oh x = 2 and plugging it in but I am so lost on how they are getting that random value!!

Their Solution Here