Answer
$x=\frac{2}{3}$.
Work Step by Step
The given polynomial is
$\Rightarrow -\frac{4}{3}x+\frac{4}{9}=-x^2$
Add $x^2$ to each side.
$\Rightarrow -\frac{4}{3}x+\frac{4}{9}+x^2=-x^2+x^2$
Simplify.
$\Rightarrow x^2-\frac{4}{3}x+\frac{4}{9}=0$
Write the the polynomial as $a^2-2ab+b^2$.
$\Rightarrow x^2-2(x)(\frac{2}{3})+(\frac{2}{3})^2=0$.
Use perfect square trinomial pattern
$a^2-2ab+b^2=(a-b)^2$.
We have $a=x$ and $b=\frac{2}{3}$.
$\Rightarrow (x-\frac{2}{3})^2=0$.
Use zero product property.
$\Rightarrow x-\frac{2}{3}=0$.
Solve for $x$.
$\Rightarrow x=\frac{2}{3}$.
Hence, the solution is $x=\frac{2}{3}$.
