Misplaced Signs

Instead of writing,$a \times (b+c) = a \times b + a \times c$, Joe by mistakenly swapped the $\times$ and + signs on the left hand side. The equation became, $a+(b \times c)= a \times b + a \times c$ ? Joe somehow knew the value of a, but forgot the values of b and c such that the equation is satisfied. Can you help him find how many ordered pairs $(b,c)$ satisfy the above equation? If there ex