Zero Product Property

Introduction

So new to me this one but obvious

a * b = 0, then either a = 0 or  b = 0

So given

3x² - 27 = 0 

I would do this which apparently is solving it numerically

3x² = 27
 x² = 9
 x  = 3

But they solved it algebraically using Zero Product Property

 3(x²-9) = 0
 3(x+3)(x-3) =0

Therefore

 x+3 = 0 and x -3 = 0

So needed to look into this