#### Answer

$x=\dfrac{4}{5}$

#### Work Step by Step

The factored form of the given expression, $
25x^2-40x+16=0
$, is
\begin{array}{}
(5x-4)(5x-4)=0
\\\\
(5x-4)^2=0
.\end{array}
Taking the square root of both sides, then,
\begin{array}{l}
5x-4=\pm\sqrt{0}
\\\\
5x-4=0
\\\\
5x=0+4
\\\\
5x=4
\\\\
x=\dfrac{4}{5}
\end{array}