Solution:
Simply by equating both sides we can get the value of $x$.
$\begin{array}{l}
2 x^{2}+2 x-2\left(x^{2}+4 x+3\right)=-12 \\
\Rightarrow-6 x-6=-12 \\
\Rightarrow-6 x=-6 \\
\Rightarrow x=1
\end{array}$
If $\left|\begin{array}{cc}2 x & x+3 \\ 2(x+1) & x+1\end{array}\right|=\left|\begin{array}{ll}1 & 5 \\ 3 & 3\end{array}\right|$, write the value of $x$.
If $\left|\begin{array}{cc}2 x & x+3 \\ 2(x+1) & x+1\end{array}\right|=\left|\begin{array}{ll}1 & 5 \\ 3 & 3\end{array}\right|$, write the value of $x$.