Đáp án:

 $a) {\left[\begin{aligned}x=0\\x=13\end{aligned}\right.}\\
c)
 {\left[\begin{aligned}x=0\\x=-1\end{aligned}\right.}\\
e)  {\left[\begin{aligned}x=\frac{2}{3}\\x=-9\end{aligned}\right.}\\
g)  {\left[\begin{aligned}x=0\\x=1\end{aligned}\right.}\\
b)  {\left[\begin{aligned}x=2000\\x=\frac{1}{5}\end{aligned}\right.}\\
d) x=-2\\
f) {\left[\begin{aligned}x=0\\x=2\\x=3\end{aligned}\right.}\\
h) x=10\\
d)  x=0$

Giải thích các bước giải:

 $a)x^2-13x=0\Leftrightarrow x(x-13)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x-13=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=13\end{aligned}\right.}\\
c)
x+1=(x+1)^2\\
\Leftrightarrow x+1-(x+1)^2=0\\
\Leftrightarrow (x+1)(1-x-1)=0\\
\Leftrightarrow (x+1).(-x)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x+1=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=-1\end{aligned}\right.}\\
e) 9(3x-2)=x(2-3x)\\
\Leftrightarrow 9(3x-2)-x(2-3x)=0\\
\Leftrightarrow 9(3x-2)+x(3x-2)=0\\
\Leftrightarrow (3x-2)(9+x)=0\\
\Leftrightarrow {\left[\begin{aligned}3x-2=0\\9+x=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}3x=2\\x=-9\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=\frac{2}{3}\\x=-9\end{aligned}\right.}\\
g) x^3=x^2\\
\Leftrightarrow x^3-x^2=0\\
\Leftrightarrow x^2(x-1)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x-1=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=1\end{aligned}\right.}\\
b) 5x(x-2000)-x+2000=0\\
\Leftrightarrow 5x(x-2000)-(x-2000)=0\\
\Leftrightarrow (x-2000)(5x-1)=0\\
\Leftrightarrow {\left[\begin{aligned}x-2000=0\\5x-1=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=2000\\5x=1\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=2000\\x=\frac{1}{5}\end{aligned}\right.}\\
d)
(x+2)^2-(x+2)(x-2)=0\\
\Leftrightarrow (x+2)(x+2-x+2)=0\\
\Leftrightarrow (x+2).4=0\\
\Leftrightarrow x+2=0\\
\Leftrightarrow x=-2\\
f)
x^2(x-2)-3x(x-2)=0\\
\Leftrightarrow x(x-2)(x-3)=0\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x-2=0\\x-3=0\end{aligned}\right.}\\
\Leftrightarrow {\left[\begin{aligned}x=0\\x=2\\x=3\end{aligned}\right.}\\
h) x(x^2+1)=10(x^2+1)\\
\Leftrightarrow x(x^2+1)-10(x^2+1)=0\\
\Leftrightarrow (x^2+1)(x-10)=0\\
\Leftrightarrow {\left[\begin{aligned}x^2+1=0(VN)\\x-10=0\end{aligned}\right.}\\
\Leftrightarrow x-10=0\\
\Leftrightarrow x=10\\
d) x^3+x=0\\
\Leftrightarrow x(x^2+1)=0\\
\Leftrightarrow {\left[\begin{aligned}x^2+1=0(VN)\\x=0\end{aligned}\right.}\\
\Leftrightarrow x=0$