Solve the equation $(2x^2-3x+1)(2x^2+5x+1)=9x^2$
Solution 1:
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?
Solution 2:
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.
Solution 3:
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?