1. **State the problem:** Simplify and verify the equation $x^2 + 8x + 16 - 2x - 8 + 7 = x^2 + 6x + 23$. 2. **Combine like terms on the left side:** $$x^2 + 8x + 16 - 2x - 8 + 7 = x^2 + (8x - 2x) + (16 - 8 + 7)$$ 3. **Simplify the terms:** $$x^2 + 6x + 15$$ 4. **Rewrite the equation:** $$x^2 + 6x + 15 = x^2 + 6x + 23$$ 5. **Subtract $x^2 + 6x$ from both sides:** $$\cancel{x^2} + \cancel{6x} + 15 = \cancel{x^2} + \cancel{6x} + 23$$ 6. **Simplify:** $$15 = 23$$ 7. **Conclusion:** Since $15 \neq 23$, the original equation is not true for any value of $x$. **Final answer:** The equation has no solution because it simplifies to a false statement.