The Bare X

In $x\left(x+2\right) = 0$, the factors are $x$ and $x+2$. Set each factor equal to zero: $x = 0$ or $x+2 = 0$. The solutions are 0 and -2.

Substitute $x = 0$ into the original equation. You get $0\left(0+2\right) = 0$, so 0 is a solution. Include this case as well as $x = -2$.

The single letter $x$ in front of the parentheses is a factor too. Include it when you split the equation. It gives the solution $x = 0$. The other factor gives the second solution. Check each answer by substituting it into the original equation.