jmc

From the definition of $A♣B$, we can rewrite the equation as:

$$\begin{array}{rl}A♣4=3A+2(4)+5& =58\\ \Rightarrow 3A+13& =58\\ \Rightarrow 3A& =45\\ \Rightarrow A& =15\end{array}$$The final value of $A$ is $\boxed{15}$.