Although cleansing the mind of ego-driven desire is by no means this simple, below is a fun visual representation of the Buddhist perspective on the root causes that result in our emotional suffering.
Also, working to diminish the influence of the ego & the things it wants isn't a path to "Happiness". That is NOT the goal. 'Inner peace' is a more accurate consequence of this work- since 'happiness' is just another aspect of our fluctuating spectrum of emotional states. The temporary feeling of 'happiness' invariably leads to a sense of loss, once we stop feeling happy.