\(\left(x-2\right)^2-\left(x+1\right)\left(x+3\right)=-7\)
\(\Leftrightarrow x^2-4x+4-\left(x^2+3x+x+3\right)=-7\)
\(\Leftrightarrow x^2-4x+4-x^2-4x-3=-7\)
\(\Leftrightarrow-8x+1=-7\)
\(\Leftrightarrow8x=7+1\)
\(\Leftrightarrow8x=8\)
\(\Leftrightarrow x=\dfrac{8}{8}\)
\(\Leftrightarrow x=1\)
__________
\(8x^2-8x+2=0\)
\(\Leftrightarrow2\left(4x^2-4x+1\right)=0\)
\(\Leftrightarrow4x^2-4x+1=0\)
\(\Leftrightarrow\left(2x-1\right)^2=0\)
\(\Leftrightarrow2x-1=0\)
\(\Leftrightarrow2x=1\)
\(\Leftrightarrow x=\dfrac{1}{2}\)
______________
\(x^3+\left(x+3\right)\left(x-9\right)=-27\)
\(\Leftrightarrow x^3+x^2-9x+3x-27=-27\)
\(\Leftrightarrow x^3+x^2-6x=-27+27\)
\(\Leftrightarrow x^3+x^2-6x=0\)
\(\Leftrightarrow x\left(x^2+x-6\right)=0\)
\(\Leftrightarrow x\left(x-2\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-3\end{matrix}\right.\)
____________________
\(5x\left(x-3\right)-2x+6=0\)
\(\Leftrightarrow5x\left(x-3\right)-\left(2x-6\right)=0\)
\(\Leftrightarrow5x\left(x-3\right)-2\left(x-3\right)=0\)
\(\Leftrightarrow\left(5x-2\right)\left(x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=2\\x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=3\end{matrix}\right.\)
_____________
\(x^2-9-4\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-3\right)-4\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-3-4\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=7\end{matrix}\right.\)
____________
\(6x\left(x-1999\right)-x+1999=0\)
\(\Leftrightarrow6x\left(x-1999\right)-\left(x-1999\right)=0\)
\(\Leftrightarrow\left(x-1999\right)\left(6x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}6x=1\\x=1999\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{6}\\x=1999\end{matrix}\right.\)
