\(a,x^2-5x=0\\ \Leftrightarrow x\left(x-5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\\ ---\\ b,\left(x+1\right)^2=x+1\\ \Leftrightarrow x^2+2x+1-x-1=0\\ \Leftrightarrow x^2+x=0\\ \Leftrightarrow x\left(x+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-1\end{matrix}\right.\\ ---\\ c,x^2+4x-12=0\\ \Leftrightarrow x^2+6x-2x-12=0\\ \Leftrightarrow x\left(x+6\right)-2\left(x+6\right)=0\\ \left(x-2\right)\left(x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+6=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-6\end{matrix}\right.\\ d,\left(x+1\right)\left(x+3\right)+\left(x+4\right)\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x+1+x+4\right)=0\\ \Leftrightarrow\left(x+3\right)\left(2x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+3=0\\2x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-\dfrac{5}{2}\end{matrix}\right.\)
