$$|x-3| \cdot |x-2|=|x-3|$$
How should I go about solving for x? Is there a intuitive method for solving these types of absolute value equations? I tried to plug in a 3 first:
$$|3-3| \cdot |3-2|=|3-3|$$
which ended up as
$$|0| \cdot |1|=|0| =0$$
But I don't know whether this is the way to go, whether I am doing this wrong or not so I hope someone could help me solve this.
Collect $|x-3|$ to obtain $$|x-3| \left( |x-2|-1 \right)=0$$ Now equate each factor to zero and find solutions $$x=3, x=1$$