[tex]~~~~x^4+4x^3 +4x^2 +4x +3=0\\\\\implies x^4 +x^3 +3x^3 + 3x^2 +x^2+x+3x+3=0\\\\\implies x^3(x+1) +3x^2(x+1) + x(x+1) +3(x+1)=0\\\\\implies (x+1) (x^3+3x^2 +x +3)=0\\\\\implies (x+1) \textbf{[} x^2(x+3)+(x+3)\textbf{]}=0\\\\\implies (x+1)(x+3)(x^2+1)=0\\\\\implies x = -1 ,~~ x = -3,~~ x = \pm i[/tex]
