smc

Using the FOIL method, we see that $(a+b)(a+c)=a^2+ab+ac+bc.$ We want to solve $$a+bc=a^2+ab+ac+bc$$ $$a=a^2+ab+ac$$ $$a((a+b+c)-1)=0$$ These expressions are $\boxed{\text{equal whenever }a+b+c=1}$