Question 515863
4x^(2)+16x+16=0

Factor out the GCF of 4 from each term in the polynomial.
4(x^(2))+4(4x)+4(4)=0

Factor out the GCF of 4 from 4x^(2)+16x+16.
4(x^(2)+4x+4)=0

For a polynomial of the form x^(2)+bx+c, find two factors of c (4) that add up to b (4).  In this problem 2*2=4 and 2+2=4, so insert 2 as the right hand term of one factor and 2 as the right-hand term of the other factor.
4(x+2)(x+2)=0

Combine the two common factors of (x+2) by adding the exponents.
4(x+2)^(2)=0

Divide both sides of the equation by 4.  Dividing 0 by any non-zero number is 0.
(x+2)^(2)=0

Set each of the factors of the left-hand side of the equation equal to 0.
x+2=0

Since 2 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2 from both sides.
x=-2