1. **State the problem:** Solve the equation $$e^2 + 5w = 12$$ for $w$. 2. **Identify the formula and rules:** This is a linear equation in $w$. To isolate $w$, subtract $e^2$ from both sides and then divide by 5. 3. **Isolate $w$:** $$e^2 + 5w = 12$$ Subtract $e^2$ from both sides: $$\cancel{e^2} + 5w - \cancel{e^2} = 12 - e^2$$ which simplifies to $$5w = 12 - e^2$$ 4. **Divide both sides by 5:** $$\frac{5w}{\cancel{5}} = \frac{12 - e^2}{\cancel{5}}$$ which simplifies to $$w = \frac{12 - e^2}{5}$$ 5. **Final answer:** $$w = \frac{12 - e^2}{5}$$ This means $w$ equals the quantity $12$ minus $e$ squared, all divided by 5.