Solve this
Question:

$9 x^{2}+6 x+1=0$

Solution:

Given :

$9 x^{2}+6 x+1=0$

$\Rightarrow 9 x^{2}+3 x+3 x+1=0$

$\Rightarrow 3 x(3 x+1)+1(3 x+1)=0$

$\Rightarrow(3 x+1)(3 x+1)=0$

$\Rightarrow 3 x+1=0$ or $3 x+1=0$

$\Rightarrow x=\frac{-1}{3}$ or $x=\frac{-1}{3}$

Hence, $\frac{-1}{3}$ is the root of the equation $9 x^{2}+6 x+1=0$.