Answer
The solution is $x=-3$.
Work Step by Step
Use the property $a^m = a^n \longrightarrow m=n$ to obtain:
$\begin{array}{ccc}
&2x-3&=&6+5x
\\&2x-3-2x&=&6+5x-2x
\\&-3&=&6+3x
\\&-3-6&=&6+3x-6
\\&-9&=&3x
\\&-9&=&3x
\\&\dfrac{-9}{3} &= &\dfrac{3x}{3}
\\&-3&=&x
\end{array}$
Thus, the solution is $x=-3$.