\(\left(5x-4\right)^2-16x^2=0\)
\(\Leftrightarrow\left(5x-4\right)^2-\left(4x\right)^2=0\)
\(\Leftrightarrow\left(5x-4-4x\right)\left(5x-4+4x\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(9x-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{4}{9}\end{matrix}\right.\)
\(\left(5x-4\right)^2-16x^2=0\\ \Leftrightarrow\left(5x-4\right)^2-\left(4x\right)^2=0\\ \Leftrightarrow\left(5x-4-4x\right).\left(5x-4+4x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}5x-4-4x=0\\5x-4+4x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{4}{9}\end{matrix}\right.\\ \Rightarrow S=\left\{\dfrac{4}{9};4\right\}\)