a: (x+1)(x-5)=0
=>\(\left[{}\begin{matrix}x+1=0\\x-5=0\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=-1\\x=5\end{matrix}\right.\)
b: \(\left(x+2\right)\left(-x-5\right)=0\)
=>\(-1\cdot\left(x+2\right)\left(x+5\right)=0\)
=>(x+2)(x+5)=0
=>\(\left[{}\begin{matrix}x+2=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-5\end{matrix}\right.\)
c: \(\left(x-2024\right)\left(4x+8\right)=0\)
=>\(4\cdot\left(x+2\right)\left(x-2024\right)=0\)
=>(x+2)(x-2024)=0
=>\(\left[{}\begin{matrix}x+2=0\\x-2024=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-2\\x=2024\end{matrix}\right.\)
d: (x+1)(2x-6)=0
=>2(x-3)(x+1)=0
=>(x-3)(x+1)=0
=>\(\left[{}\begin{matrix}x-3=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)
e: (2x+10)(4x+20)=0
=>\(2\left(x+5\right)\cdot4\left(x+5\right)=0\)
=>\(8\left(x+5\right)^2=0\)
=>\(\left(x+5\right)^2=0\)
=>x+5=0
=>x=-5
h: \(\left(-24+x\right)\left(4x-8\right)=0\)
=>\(4\cdot\left(x-2\right)\cdot\left(x-24\right)=0\)
=>\(\left(x-2\right)\left(x-24\right)=0\)
=>\(\left[{}\begin{matrix}x-2=0\\x-24=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=24\end{matrix}\right.\)
i: (4x-100)(3x-6)=0
=>\(\left[{}\begin{matrix}4x-100=0\\3x-6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}4x=100\\3x=6\end{matrix}\right.\)
=>\(\left[{}\begin{matrix}x=25\\x=2\end{matrix}\right.\)
k: (-7-x)(4x-36)=0
=>\(\left(-1\right)\cdot\left(x+7\right)\cdot4\left(x-9\right)=0\)
=>\(\left(x+7\right)\left(x-9\right)=0\)
=>\(\left[{}\begin{matrix}x+7=0\\x-9=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-7\\x=9\end{matrix}\right.\)