$16{x}^{2}+16x+4+4\left( 4x+2 \right)+4=0$
Distribute $4$ through the parentheses$16{x}^{2}+16x+4+16x+8+4=0$
Collect like terms$16{x}^{2}+32x+4+8+4=0$
Calculate the sum of the positive numbers$16{x}^{2}+32x+16=0$
Divide both sides of the equation by $16$${x}^{2}+2x+1=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=1,& b=2,& c=1\end{array}$
Substitute $a=1$, $b=2$ and $c=1$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -2\pm\sqrt{ {2}^{2}-4 \times 1 \times 1 } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -2\pm\sqrt{ {2}^{2}-4 \times 1 } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -2\pm\sqrt{ {2}^{2}-4 } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -2\pm\sqrt{ {2}^{2}-4 } }{ 2 }$
Evaluate the power$x=\frac{ -2\pm\sqrt{ 4-4 } }{ 2 }$
The sum of two opposites equals $0$$x=\frac{ -2\pm\sqrt{ 0 } }{ 2 }$
Any root of $0$ equals $0$$x=\frac{ -2\pm0 }{ 2 }$
Removing $0$ doesn't change the value, so remove it from the expression$x=\frac{ -2 }{ 2 }$
Any expression divided by its opposite equals $-1$$x=-1$