Solve in integers $y^2 = x^3 + (x+4)^2$
$$y^2 = x^3 + (x+4)^2$$ $$y^2 = x^3 + x^2 + 8x + 16$$ $$y^2 - x^2 = x^3 + 8x + 16$$ $$(y+x)(y-x) = x^3 + 8(x+2)$$
How to I continue? I know I should get the form $(ax^b+c)(dy^e+f) = g$ and then factor the combinations but I'm not sure how to get there. Thanks so much for the help!