a)\(\left(2x+3\right)^2-2\left(2x+3\right)\left(2x-5\right)+\left(2x-5\right)^2=x^2+6x+64\)
\(\Rightarrow\left[\left(2x+3\right)-\left(2x-5\right)\right]^2=x^2+6x+64\)
\(\Rightarrow\left(2x+3-2x+5\right)^2=x^2+6x+64\)
\(\Rightarrow8^2=x^2+6x+64\)
\(\Rightarrow64=x^2+6x+64\)
\(\Rightarrow x^2+6x=0\)
\(\Rightarrow x\left(x+6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x+6=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-6\end{matrix}\right.\)
b) \(\left(x^4+2x^3+10x-25\right):\left(x^2+5\right)=3\)
\(\Rightarrow\left(x^4+5x^2-5x^2-25+2x^3+10x\right):\left(x^2+5\right)=3\)
\(\Rightarrow\left[x^2\left(x^2+5\right)-5\left(x^2+5\right)+2x\left(x^2+5\right)\right]:\left(x^2+5\right)=3\)
\(\Rightarrow\left(x^2+5\right)\left(x^2-5+2x\right):\left(x^2+5\right)=3\)
\(\Rightarrow x^2+2x-5=3\)
\(\Rightarrow x^2+2x-5-3=0\)
\(\Rightarrow x^2+2x-8=0\)
\(\Rightarrow x^2+4x-2x-8=0\)
\(\Rightarrow x\left(x+4\right)-2\left(x+4\right)=0\)
\(\Rightarrow\left(x+4\right)\left(x-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+4=0\\x-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-4\\x=2\end{matrix}\right.\)
