\(A\left(1\right)=12.\left(1\right)^3+2.1a+a^2=12+2a+a^2\)
\(B\left(-2\right)=2.\left(-2\right)^2-\left|2a+3\right|.-2+a^2=8+2\left|2a+3\right|+a^2\)
\(A\left(1\right)=B\left(2\right)\)
\(\Leftrightarrow12+2a+a^2=8+2\left|2a+3\right|+a^2\)
\(\Leftrightarrow-2\left|2a+3\right|=-4-2a\)
\(\Leftrightarrow\left|2a+3\right|=2+a\)
\(ĐK:a\ge-2\)
\(\Leftrightarrow\left[{}\begin{matrix}2a+3=-2-a\\2a+3=2+a\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}a=-\dfrac{5}{3}\left(n\right)\\a=-1\left(n\right)\end{matrix}\right.\)
Vậy \(a=\left\{-\dfrac{5}{3};-1\right\}\)