1. **State the problem:** Solve the quadratic equation $$14x^2 - 7x + 3 = 3$$ and then solve $$14x^2 - 7x = 0$$. 2. **Simplify the first equation:** Subtract 3 from both sides to set the equation to zero: $$14x^2 - 7x + 3 - 3 = 3 - 3$$ $$14x^2 - 7x = 0$$ 3. **Notice that both equations simplify to the same quadratic:** $$14x^2 - 7x = 0$$. 4. **Factor the quadratic:** $$7x(2x - 1) = 0$$ 5. **Use the zero product property:** Set each factor equal to zero: $$7x = 0 \implies x = 0$$ $$2x - 1 = 0 \implies 2x = 1 \implies x = \frac{1}{2}$$ 6. **Final answer:** The solutions are $$x = 0$$ and $$x = \frac{1}{2}$$.