A simultaneous system of equations Solve for $a,b,c$:
\begin{align}
2ab+a+2b=24\\
2bc+b+c=52\\
2ac+2c+a=74\\
\end{align}
Solving them simultaneously is leading to very difficult situation. Plz help.

Here is a partial answer: User the first equation and third equation (add and substract) to obtain 
\begin{align}
c-b&=\frac{25}{a+1} \\
c+b&=\frac{49-a}{a+1}
\end{align}
Adding and subtracting should again give
\begin{align}
c=&\frac{1}{2}\frac{74-a}{a+1} \\
b=&\frac{1}{2}\frac{24-a}{a+1}
\end{align} 
Substituting this into the second equation should give a equation in $a$ alone which looks to be quartic. 
