Using properties of determinants, solve the following for x : $\begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $

Question

$\begin{array}{1 1} \frac{-a}{3} \\ \frac{2a}{3} \\\frac{4a}{3} \\ \frac{-2a}{3} \end{array} $