\(a,2x+5=20-3x\\ \Leftrightarrow5x=15\\ \Leftrightarrow x=3\\ b,x^2+5x+6=0\\ \Leftrightarrow x^2+2x+3x+6=0\\ \Leftrightarrow x\left(x+2\right)+3\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x+3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-2\\x=-3\end{matrix}\right.\\ c,x^3-1=\left(5+x\right)\left(x-1\right)\\ \Leftrightarrow\left(x-1\right)\left(x^2+x+1\right)-\left(5+x\right)\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x^2+x+1-5-x\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x^2-4\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\\x=-2\end{matrix}\right.\)
\(d,\left(2x-1\right)^2-\left(x+3\right)^2=0\\ \Leftrightarrow\left(2x-1-x-3\right)\left(2x-1+x+3\right)=0\\ \Leftrightarrow\left(x-4\right)\left(3x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4\\x=-\dfrac{2}{3}\end{matrix}\right.\)
\(g,x^2-3x=0\\ \Leftrightarrow x\left(x-3\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\\ h,\left(x-2\right)\left(5x+3\right)=\left(3x-8\right)\left(x-2\right)\\ \Leftrightarrow\left(x-2\right)\left(5x+3\right)-\left(3x-8\right)\left(x-2\right)=0\\ \Leftrightarrow\left(x-2\right)\left(5x+3-3x+8\right)=0\\ \Leftrightarrow\left(x-2\right)\left(2x+11\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{11}{2}\end{matrix}\right.\)
\(i,x^2-5x+4=0\\ \Leftrightarrow x^2-x-4x+4=0\\ \Leftrightarrow x\left(x-1\right)-4\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\\ k,x\left(x^2-x\right)=30x\\ \Leftrightarrow x\left(x^2-x\right)-30x=0\\ \Leftrightarrow x\left(x^2-x-30\right)=0\\ \Leftrightarrow x\left(x^2-6x+5x-30\right)=0\\ \Leftrightarrow x\left[x\left(x-6\right)+5\left(x-6\right)\right]=0\\ \Leftrightarrow x\left(x-6\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=6\\x=-5\end{matrix}\right.\)
