4w^2+16w+16=0

Solution for 4w^2+16w+16=0 equation:

Simplifying
4w2 + 16w + 16 = 0

Reorder the terms:
16 + 16w + 4w2 = 0

Solving
16 + 16w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + 4w + w2) = 0

Factor a trinomial.
4((2 + w)(2 + w)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

Simplifying
w = -2
Solution
w = {-2, -2}