$x^{2} +4 x+4=0 \ldots$ We try to separate the middle term $4 x$ to find common factors with $x^{2} $ and 4 separately:

$x^{2} +2 x+2 x+4=0 \ldots$ Here, we see that $x$ is a common factor for $x^{2} $ and $2 x_{1}$ and 2 is a common factor for $2 x$ and 4 :

$x(x+2)+2(x+2)=0 \ldots$ Here, we have $x$ times $x+2$ and

2 times $x+2$ summed up. This means that we have $x+2$

times $x+2$

$(x+2)(x+2)=0$

$(x+2) =0 \ldots$ This is true if only if $x+2$ is equal to zero.

$x+2=0$

$x=-2$