1. **State the problem:** Solve the equation $5(K+4) = 2(5K-3) + 12$ for $K$. 2. **Write the formula and rules:** Use the distributive property to expand both sides and then isolate the variable $K$. 3. **Expand both sides:** $$5(K+4) = 5K + 20$$ $$2(5K-3) + 12 = 10K - 6 + 12 = 10K + 6$$ 4. **Rewrite the equation:** $$5K + 20 = 10K + 6$$ 5. **Bring all terms involving $K$ to one side and constants to the other:** $$5K + 20 = 10K + 6$$ $$5K - 10K = 6 - 20$$ $$\cancel{5K} - 10K = 6 - 20$$ $$-5K = -14$$ 6. **Divide both sides by $-5$ to solve for $K$:** $$K = \frac{-14}{-5}$$ $$K = \cancel{\frac{-14}{-5}} = \frac{14}{5}$$ 7. **Final answer:** $$K = \frac{14}{5}$$