1. **State the problem:** Solve the equation $a+b+2ab=8$ for the expression $a+b$. 2. **Analyze the equation:** The equation is $a+b+2ab=8$. We want to find $a+b$ in terms of known quantities or constants. 3. **Use substitution:** Let $S = a+b$ and $P = ab$. Then the equation becomes: $$S + 2P = 8$$ 4. **Note:** We have one equation with two unknowns $S$ and $P$. Without additional information, we cannot find a unique value for $S$. 5. **Express $P$ in terms of $S$:** $$2P = 8 - S \implies P = \frac{8 - S}{2}$$ 6. **Conclusion:** The value of $a+b$ (which is $S$) cannot be uniquely determined from the given equation alone. It depends on the value of $ab$ (which is $P$). The equation relates $S$ and $P$ by: $$S + 2P = 8$$ Therefore, $a+b$ can be any value $S$ such that there exists $P$ satisfying $P = \frac{8 - S}{2}$. If you have more information or constraints, please provide them to solve for $a+b$ uniquely.