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Question:

If $\left|\begin{array}{ll}2 x+5 & 3 \\ 5 x+2 & 9\end{array}\right|=0$, find $x$

Solution:

$\left|\begin{array}{ll}2 x+5 & 3 \\ 5 x+2 & 9\end{array}\right|=0$

$\Rightarrow 9(2 x+5)-3(5 x+2)=0$

$\Rightarrow 18 x+45-15 x-6=0$

$\Rightarrow 3 x+39=0$

$\Rightarrow 3 x=-39$

$\Rightarrow x=\frac{-39}{3}=-13$

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