\(1,\left(x-4\right)^2-36=0\)
\(\Leftrightarrow\left(x-4-6\right)\left(x-4+6\right)=0\)
\(\Leftrightarrow\left(x-10\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)
\(2,x^2-25-\left(x+5\right)^2\)
\(=\left(x-5\right)\left(x+5\right)-\left(x+5\right)^2\)
\(=\left(x+5\right)\left(x-5-x-5\right)\)
\(=-10\left(x+5\right)\)
\(3,\left(2x-3\right)^2=\left(x+5\right)^2\)
\(\Leftrightarrow\left(2x-3\right)^2-\left(x+5\right)^2=0\)
\(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
\(\Leftrightarrow\left(x-8\right)\left(3x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
\(5,\left(x+8\right)^2=191\)
\(\Leftrightarrow\left(x+8\right)^2-191=0\)
\(\Leftrightarrow\left(x+8-\sqrt{191}\right)\left(x+8+\sqrt{191}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{191}-8\\x=-\sqrt{191}-8\end{matrix}\right.\)
\(6,x^2+4-\left(x-2\right)^2=0\)
\(\Leftrightarrow x^2+4-x^2+4x-4=0\)
\(\Leftrightarrow4x=0\Leftrightarrow x=0\)
