$$4x(8x-5)=4x(yx-10)$$
$\left\{\begin{matrix}y=8+\frac{5}{x}\text{, }&x\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$
$$x\left(8x-5\right)=x\left(yx-10\right)$$
$$8x^{2}-5x=x\left(yx-10\right)$$
$$8x^{2}-5x=yx^{2}-10x$$
$$yx^{2}-10x=8x^{2}-5x$$
$$yx^{2}=8x^{2}-5x+10x$$
$$yx^{2}=8x^{2}+5x$$
$$x^{2}y=8x^{2}+5x$$
$$\frac{x^{2}y}{x^{2}}=\frac{x\left(8x+5\right)}{x^{2}}$$
$$y=\frac{x\left(8x+5\right)}{x^{2}}$$
$$y=8+\frac{5}{x}$$
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$\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x=-\frac{5}{8-y}\text{, }&y\neq 8\end{matrix}\right.$
