a) \(3x\left(x-7\right)+x-7=0\\ \Rightarrow\left(3x+1\right)\left(x-7\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{1}{3}\\x=7\end{matrix}\right.\)
b) \(15x-5+6x^2-2x=0\\ \Rightarrow5\left(3x-1\right)+2x\left(3x-1\right)=0\\ \Rightarrow\left(5+2x\right)\left(3x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\)
c) \(x^2-6x+9=16\\ \Rightarrow\left(x-3\right)^2=16\\ \Rightarrow\left[{}\begin{matrix}x-3=-16\\x-3=16\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-13\\x=19\end{matrix}\right.\)
d) \(\left(x+2\right)^2-x^2+4=0\\ \Rightarrow\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\\ \Rightarrow\left(x+2\right)\left(x+2-x+2\right)=0\\ \Rightarrow4\left(x+2\right)=0\\ \Rightarrow x=-2\)
e) \(3x^3-27=0\\ \Rightarrow x^3=9\\ \Rightarrow x=\sqrt[3]{9}\)
f) \(36-\left(x+2\right)^2=0\\ \Rightarrow\left(x+2\right)^2=36\\ \Rightarrow\left[{}\begin{matrix}x+2=-6\\x+2=6\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=-8\\x=4\end{matrix}\right.\)
g) \(5x^3-125x=0\\ \Rightarrow5x\left(x^2-25\right)=0\\ \Rightarrow5x\left(x-5\right)\left(x+5\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
h) \(x^2-9+2\left(x+3\right)=0\\ \Rightarrow\left(x-3\right)\left(x+3\right)+2\left(x+3\right)=0\\ \Rightarrow\left(x+3\right)\left(x-1\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
\(a,\Leftrightarrow\left(x-7\right)\left(3x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-\dfrac{1}{3}\end{matrix}\right.\\ b,\Leftrightarrow5\left(3x-1\right)+2x\left(3x-1\right)=0\\ \Leftrightarrow\left(5+2x\right)\left(3x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{5}{2}\\x=\dfrac{1}{3}\end{matrix}\right.\\ c,\Leftrightarrow\left(x-3\right)^2-16=0\\ \Leftrightarrow\left(x-3-4\right)\left(x-3+4\right)=0\\ \Leftrightarrow\left(x-7\right)\left(x+1\right)\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\\ d,\Leftrightarrow\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left(x+2\right)\left(x+2-x+2\right)=0\\ \Leftrightarrow4\left(x+2\right)=0\Leftrightarrow x=-2\\ e,\Leftrightarrow3\left(x^3-9\right)=0\\ \Leftrightarrow x^3=9\Leftrightarrow x=\sqrt[3]{9}\\ f,\Leftrightarrow\left(6-x-2\right)\left(6+x+2\right)=0\\ \Leftrightarrow\left(4-x\right)\left(x+8\right)=0\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-8\end{matrix}\right.\)
\(g,\Leftrightarrow5x\left(x^2-25\right)=0\\ \Leftrightarrow5x\left(x-5\right)\left(x+5\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\\ h,\Leftrightarrow\left(x-3\right)\left(x+3\right)+2\left(x+3\right)=0\\ \Leftrightarrow\left(x+3\right)\left(x-1\right)=0\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=1\end{matrix}\right.\)
