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?

Hint:
As $x\ne0$ we can divide both sides by $x^2$ to find
$$(a-3)(a+5)=9\iff a^2+2a-24=0$$ where $2x+\dfrac1x=a$
Can you take it home from here?
