a: \(x^2+16x=0\)
=>\(x\left(x+16\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x+16=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-16\end{matrix}\right.\)
b; \(3x\left(x+5\right)-x-5=0\)
=>\(3x\left(x+5\right)-\left(x+5\right)=0\)
=>\(\left(x+5\right)\left(3x-1\right)=0\)
=>\(\left[{}\begin{matrix}x+5=0\\3x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=\dfrac{1}{3}\end{matrix}\right.\)
c: \(x^2-x+3\left(x-1\right)=0\)
=>\(\left(x^2-x\right)+3\left(x-1\right)=0\)
=>\(x\left(x-1\right)+3\left(x-1\right)=0\)
=>(x-1)(x+3)=0
=>\(\left[{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
d: \(3x\left(x+1\right)-2x\left(x+2\right)=-x-1\)
=>\(3x^2+3x-2x^2-4x+x+1=0\)
=>\(x^2+1=0\)
=>\(x^2=-1\)(vô lý)
=>\(x\in\varnothing\)
e: \(4x\left(x-2019\right)-x+2019=0\)
=>\(4x\left(x-2019\right)-\left(x-2019\right)=0\)
=>\(\left(x-2019\right)\left(4x-1\right)=0\)
=>\(\left[{}\begin{matrix}x-2019=0\\4x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2019\\x=\dfrac{1}{4}\end{matrix}\right.\)
f: \(\left(x+1\right)^3-4=x^2\left(x+3\right)\)
=>\(x^3+3x^2+3x+1-4=x^3+3x^2\)
=>3x-3=0
=>3x=3
=>x=1
g: \(x\left(x-3\right)-5\left(x-3\right)=0\)
=>\(\left(x-3\right)\left(x-5\right)=0\)
=>\(\left[{}\begin{matrix}x-3=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=5\end{matrix}\right.\)
