\(4x^2+4x+1=x^2\\\Leftrightarrow 3x^2+4x+1=0\\\Leftrightarrow3x^2+3x+x+1=0\\\Leftrightarrow 3x(x+1)+(x+1)=0\\\Leftrightarrow (3x+1)(x+1)=0 \\\Leftrightarrow \left[\begin{array}{} 3x+1=0\\ x+1=0 \end{array} \right. \Leftrightarrow \left[\begin{array}{} x=-\frac13\\ x=-1 \end{array}\right.\)