Solve the equation $(2x^2-3x+1)(2x^2+5x+1)=9x^2$ Solve the equation $$(2x^2-3x+1)(2x^2+5x+1)=9x^2$$
The given equation is equivalent to $$4x^4+4x^3-11x^2+2x+1=9x^2\\4x^4+4x^3-20x^2+2x+1=0$$ which, unfortunately, has no rational roots. What else can I try?

We have, $$((2x^2+x+1)-4x)((2x^2+x+1)+4x)=9x^2$$
$$(2x^2+x+1)^2-16x^2=9x^2\;\Rightarrow\; (2x^2+x+1)^2=(5x)^2$$
Hence,  $\;2x^2+x+1=\pm5x$. Can you take it from here?
