\(a,x^2-16x=0\)

\(\Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)

\(b,9x^2+6x+4y^2-8y+5=0\)

\(\Leftrightarrow\left(9x^2+6x+1\right)+4\left(y^2-2y+1\right)=0\)

\(\Leftrightarrow\left(3x+1\right)^2+4\left(y-1\right)^2=0\)

\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x+1\right)^2=0\\4\left(y-1\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{3}\\y=1\end{matrix}\right.\)

\(a,9x^2-6x+1-y^2\)

\(=\left(3x-1\right)^2-y^2\)

\(=\left(3x-1-y\right)\left(3x-1+y\right)\)

\(b,x^2-7x+10\)

\(=x^2-2x-5x+10\)

\(=x\left(x-2\right)-5\left(x-2\right)\)

\(=\left(x-2\right)\left(x-5\right)\)

\(x+25\%=\dfrac{3}{4}\)

\(\Rightarrow x+\dfrac{1}{4}=\dfrac{3}{4}\)

\(\Rightarrow x=\dfrac{1}{2}\)

\(4⋮\left(n+1\right)\)

\(\Rightarrow\left(n+1\right)\inƯ\left(4\right)=\left\{1;-1;2;-2;4;-4\right\}\)

\(\Rightarrow n\in\left\{0;-2;1;-3;3;-5\right\}\)