1)  x³ + ²4x + 4x  = 0
=> x ( x² + 4x + 4 ) = 0
=> x ( x + 2 )² = 0
=> \(\left[ \begin{array}{l}x=0\\x+2=0\end{array} \right.\) 
=> \(\left[ \begin{array}{l}x=0\\x=-2\end{array} \right.\) 
2) ( x + 3 )² - 4 = 0
    ( x + 3 )²       = 4
=> ( x + 3 )²     = ±2²
=>   x + 3         = ±2
=> \(\left[ \begin{array}{l}x+3=2\\x+3=-2\end{array} \right.\) 
=> \(\left[ \begin{array}{l}x=-1\\x=-5\end{array} \right.\)