1. The problem asks to factorize the quadratic equation $$4x^2 - 12x + 9$$ and solve for $$x$$. 2. Recognize that the equation is of the form $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. Compare $$4x^2 - 12x + 9$$ with $$a^2 - 2ab + b^2$$: - $$a^2 = 4x^2$$ so $$a = 2x$$. - $$b^2 = 9$$ so $$b = 3$$. - Check the middle term: $$-2ab = -2 \times 2x \times 3 = -12x$$, which matches. 4. Therefore, the factorization is: $$4x^2 - 12x + 9 = (2x - 3)^2$$. 5. To solve for $$x$$, set the factorized form equal to zero: $$(2x - 3)^2 = 0$$. 6. This implies: $$2x - 3 = 0$$. 7. Solve for $$x$$: $$2x = 3$$ $$x = \frac{3}{2}$$. Final answer: $$x = \frac{3}{2}$$.