$$\begin{gathered} a, 8x^2-4x=0<=>4x.\left(2x-1\right)=0 \\ <=>4x=0 hoặc 2x-1=0 \\ <=>x=0 hoặc x=\frac{1}{2} \\ Vậy S=\left\{0;\frac{1}{2}\right\} \\ b, 5x\left(x-3\right)+7\left(x-3\right)=0 \\ <=>\left(x-3\right)\left(5x+7\right)=0 \\ <=>x-3=0 hoặc 5x+7=0 \\ <=>x=3 hoặc x=\frac{-7}{5} \\ Vậy\hspace{0.17em}S=\left\{\frac{-7}{5};3\right\} \\ c, 7x\left(x-2004\right)-x+2004=0 \\ <=>7x\left(x-2004\right)-\left(x-2004\right)=0<=>\left(x-2004\right)\left(7x-1\right)=0 \\ <=>x-2004=0 hoặc 7x-1=0 \\ <=>x=2004 hoặc x=\frac{1}{7} \\ Vậy S=\left\{2004;\frac{1}{7}\right\} \end{gathered}$$

$$\begin{gathered} d, 2x^2=x<=>2x^2-x=0<=>x.\left(2x-1\right)=0 \\ <=>x=0 hoặc 2x-1=0 \\ <=>x=0 hoặc x=\frac{1}{2} \\ Vậy S=\left\{0;\frac{1}{2}\right\} \\ e, x^2-5x=0<=>x.\left(x-5\right)=0 \\ <=>x=0 hoặc x-5=0<=>x=0 hoặc x=5 \\ Vậy S=\left\{0;5\right\} \\ f, x^2+5x=0<=>x\left(x+5\right)=0 \\ <=>x=0 hoặc x+5=0 \\ <=>x=0 hoặc x=-5 \\ Vậy S=\left\{-5;0\right\} \end{gathered}$$

$$\begin{gathered} g, {\left(x+1\right)}^2-\left(x+1\right)\left(x-1\right)=0 \\ <=>x^2+2x+1-x^2+1=0 \\ <=>2x+2=0<=>x=-1 \\ Vậy\hspace{0.17em}S=\left\{-1\right\} \end{gathered}$$.

\[\begin{array}{l}
a,{\rm{ }}8{x^2} - 4x = 0\\
\Leftrightarrow 4x\left( {2x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
4x = 0\\
2x - 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = \frac{1}{2}
\end{array} \right.\\
vay:S = \{ 0;\frac{1}{2}\} \\
b,{\rm{ }}5x\left( {x - 3} \right) + 7\left( {x - 3} \right) = 0\\
\Leftrightarrow \left( {x - 3} \right)\left( {5x + 7} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 3 = 0\\
5x + 7 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = \frac{{ - 7}}{5}
\end{array} \right.\\
vay:S = \{ 3;\frac{{ - 7}}{5}\} \\
c,{\rm{ }}7x\left( {x - 2004} \right) - {\rm{ }}x + 2004 = 0\\
\Leftrightarrow 7x\left( {x - 2004} \right) - \left( {x - 2004} \right) = 0\\
\Leftrightarrow \left( {x - 2004} \right)\left( {7x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2004 = 0\\
7x - 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2004\\
x = \frac{1}{7}
\end{array} \right.\\
Vay:S = \{ 2004;\frac{1}{7}\} \\
d,{\rm{ }}2{x^2} = x\\
\Leftrightarrow 2{x^2} - x = 0\\
\Leftrightarrow x\left( {2x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
2x - 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = \frac{1}{2}
\end{array} \right.\\
vay:S = \{ 0;\frac{1}{2}\} \\
e,{\rm{ }}x{{\rm{ }}^2} - 5x = 0\\
\Leftrightarrow x\left( {x - 5} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x - 5 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 5
\end{array} \right.\\
vay:S = \{ 0;5\} \\
f,{\rm{ }}{x^2} + 5x = 0\\
\Leftrightarrow x\left( {x + 5} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x + 5 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = - 5
\end{array} \right.\\
Vay:S = \{ 0; - 5\} \\
g,{\rm{ }}{\left( {x + 1} \right)^2}{\rm{ }} - {\rm{ }}\left( {x + 1} \right)\left( {x - 1} \right) = 0\\
\Leftrightarrow \left( {x + 1} \right)\left( {x + 1 - x + 1} \right) = 0\\
\Leftrightarrow 2\left( {x + 1} \right) = 0\\
\Leftrightarrow x + 1 = 0\\
\Leftrightarrow x = - 1\\
vay:x = - 1
\end{array}\]