 made the wrong assumption that
  \( x \ne 0 \).  If we want to consider the possibility of
  \( x = 0 \) as a solution, then we cannot divide both sides of the
  equation by \( x \).  Division by \( 0 \) is undefined in
  arithmetic.  This is why the typical way to solve such an equation
  is to bring all terms involving \( x \) to one side of the equation
  and then solve it.  For example,

  \begin{align*}
    x(x - 2) = 3x
    &amp; \iff x(x - 2) - 3x = 0 \\
    &amp; \iff x^2 - 2x - 3x = 0 \\
    &amp;