1. **State the problem:** Solve the equation $ (x+5)(x-5) = x(x-4) + 7 $ for $x$. 2. **Recall the formula:** Use the distributive property (FOIL) to expand both sides. 3. **Expand the left side:** $$ (x+5)(x-5) = x^2 - 5x + 5x - 25 = x^2 - 25 $$ 4. **Expand the right side:** $$ x(x-4) + 7 = x^2 - 4x + 7 $$ 5. **Set the equation:** $$ x^2 - 25 = x^2 - 4x + 7 $$ 6. **Subtract $x^2$ from both sides:** $$ -25 = -4x + 7 $$ 7. **Isolate $x$:** $$ -25 - 7 = -4x $$ $$ -32 = -4x $$ 8. **Divide both sides by $-4$:** $$ x = \frac{-32}{-4} = 8 $$ **Final answer:** $$ x = 8 $$