In solving the equation (x + 3)(x – 3) = -8, Eric stated that the solution would be

x + 3 = -8 => x = -11
or
(x – 3) = -8 => x = -5
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.

in equation (x + 3)(x – 3) = -8
we can not say x+3=-8 nor x-3=8
but if (x + 3)(x – 3) = 0 we can
because if x+3=0 means 0(x-3)=0

In solving equation above you should simplify is first
(x+3)(x-3)=-8
x^2 -3x +3x -9 =-8
x^2 -9 +8=0
x^2 -1 =0
factor them
(x-1)(x+1)=0
x-1=0 => x=1
x+1=0 => x=-1

when you say (x+3)=-8=> x=-11
you should say after
x-3=1 =>x=4
the right way to resolve the equation is:
(x+3)(x-3)=-8
x^2-9=-8
x^2=1
x=+/-1