1. **State the problem:** Solve the polynomial equation $$6x^2 - 6 = 0$$. 2. **Write the formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we isolate $$x^2$$ and then take the square root of both sides. 3. **Isolate the quadratic term:** $$6x^2 - 6 = 0$$ Add 6 to both sides: $$6x^2 = 6$$ 4. **Divide both sides by 6:** $$\frac{6x^2}{\cancel{6}} = \frac{6}{\cancel{6}}$$ which simplifies to $$x^2 = 1$$ 5. **Take the square root of both sides:** $$x = \pm \sqrt{1}$$ 6. **Simplify the square root:** $$x = \pm 1$$ 7. **Final answer:** The solutions to the polynomial equation are $$x = 1$$ and $$x = -1$$.