Step 1 :The given trinomial is a quadratic equation of the form \(ax^2 + bx + c\).
Step 2 :To factorize it, we can use the formula for factoring a perfect square trinomial, which is \(a^2 - 2ab + b^2 = (a - b)^2\).
Step 3 :Here, we can see that \(a = 6x\), \(b = 6\), and the trinomial is a perfect square.
Step 4 :So, we can factorize it as \((6x - 6)^2\).
Step 5 :The factored form of the trinomial \(36 x^{2}-72 x+36\) is \(\boxed{36(x - 1)^{2}}\).