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?

Recall that your last equation can be written as the product of two polynomials of degree two, $$(2x^2-4x+1)(2x^2+6x+1)=0$$ It is then easy to find the roots of both polynomials.
