#### Answer

$x=\left\{ \dfrac{2}{3} \right\}$

#### Work Step by Step

The two numbers whose product is $ac=
9(4)=36
$ and whose sum is $b=
-12
$ are $\{
-6,-6
\}$. Using these two numbers to decompose the middle term of the given equation, $
9x^2-12x+4=0
,$ results to
\begin{array}{l}\require{cancel}
9x^2-6x-6x+4=0
\\\\
(9x^2-6x)-(6x-4)=0
\\\\
3x(3x-2)-2(3x-2)=0
\\\\
(3x-2)(3x-2)=0
.\end{array}
Equating each factor to zero (or the Zero-Factor Property), the solutions to the given equation are
\begin{array}{l}\require{cancel}
3x-2=0
\\\\
3x=2
\\\\
x=\dfrac{2}{3}
,\\\\\text{OR}\\\\
3x-2=0
\\\\
3x=2
\\\\
x=\dfrac{2}{3}
.\end{array}
Hence, the solution is $
x=\left\{ \dfrac{2}{3} \right\}
.$