a) $x^3-\dfrac{1}{9}x=0$

$\Rightarrow x\left(x^2-\dfrac{1}{9}\right)=0$

$\Rightarrow x\left(x-\dfrac{1}{3}\right)\left(x+\dfrac{1}{3}\right)=0$

$\Rightarrow\left[{}\begin{matrix}x=0\\x-\dfrac{1}{3}=0\Leftrightarrow x=\dfrac{1}{3}\\x+\dfrac{1}{3}=0\Leftrightarrow x=-\dfrac{1}{3}\end{matrix}\right.$

b) $x\left(x-3\right)+x-3=0$

$\Rightarrow\left(x-3\right)\left(x+1\right)=0$

$\Rightarrow\left[{}\begin{matrix}x-3=0\Rightarrow x=3\\x+1=0\Rightarrow x=-1\end{matrix}\right.$

c) $2x-2y-x^2+2xy-y^2=0$ (thêm đề)

$\Rightarrow2\left(x-y\right)-\left(x-y\right)^2=0$

$\Rightarrow\left(x-y\right)\left(2-x+y\right)=0$

$\Rightarrow\left\{{}\begin{matrix}x-y=0\Rightarrow x=y\\2-x+y=0\Rightarrow x-y=2\end{matrix}\right.$

$\Rightarrow\left\{{}\begin{matrix}x=y\left(1\right)\\\left(1\right)\Rightarrow x-x=2\left(loại\right)\end{matrix}\right.$

d) $x^2\left(x-3\right)+27-9x=0$

$\Rightarrow x^2\left(x-3\right)+\left(x-3\right).9=0$

$\Rightarrow\left(x-3\right)\left(x^2+9\right)=0$

$\Rightarrow x-3=0\Rightarrow x=3.$