\(\left(2x+3\right)\left(x-4\right)=x^2-3x-4\)
\(\Leftrightarrow\left(2x+3\right)\left(x-4\right)=x^2+x-4x-4\)
\(\Leftrightarrow\left(2x+3\right)\left(x-4\right)=\left(x-4\right)\left(x+1\right)\)
\(\Leftrightarrow2x+3=\frac{\left(x-4\right)\left(x+1\right)}{x-4}\)
\(\Leftrightarrow2x+3=x+1\)
\(\Leftrightarrow2x-x=1-3\)
\(\Leftrightarrow x=-2\)