Chapter 5 - Section 5.8 - Solving Equations by Factoring and Problem Solving - Exercise Set - Page 323: 39

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

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}