1. **State the problem:** Simplify and solve the equation $$4x - 9^2 + 6 = 10$$ for $x$. 2. **Rewrite the equation:** Note that $9^2$ means $9$ squared, which is $81$. So the equation becomes: $$4x - 81 + 6 = 10$$ 3. **Simplify constants:** Combine $-81$ and $+6$: $$4x - 75 = 10$$ 4. **Isolate the term with $x$:** Add $75$ to both sides: $$4x - 75 + 75 = 10 + 75$$ $$4x = 85$$ 5. **Solve for $x$:** Divide both sides by $4$: $$x = \frac{85}{4}$$ 6. **Final answer:** $$x = \frac{85}{4}$$ or $x = 21.25$. This means the value of $x$ that satisfies the equation is $21.25$.