\(8a\left(a+2b\right)=5b\left(b+2a\right)\)
\(\Leftrightarrow8a^2+16ab=5b^2+10ab\)
\(\Leftrightarrow8a^2+6ab-5b^2=0\)
\(\Leftrightarrow\left(2a-b\right)\left(4a+5b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=\dfrac{b}{2}\\a=-\dfrac{5b}{4}\end{matrix}\right.\)
\(8a\left(a+2b\right)=5b\left(2a+b\right)\)
\(\Leftrightarrow8a^2+16ab-10ab-5b^2=0\)
\(\Leftrightarrow8a^2+6ab-5b^2=0\)
\(\Leftrightarrow8a^2+10ab-4ab-5b^2=0\)
\(\Leftrightarrow\left(4a+b\right)\left(2a-b\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}a=-\dfrac{b}{4}\\a=\dfrac{b}{2}\end{matrix}\right.\)
