0=z^2+8z+16

Solution for 0=z^2+8z+16 equation:

Simplifying
0 = z2 + 8z + 16

Reorder the terms:
0 = 16 + 8z + z2

Solving
0 = 16 + 8z + z2

Solving for variable 'z'.

Combine like terms: 0 + -16 = -16
-16 + -8z + -1z2 = 16 + 8z + z2 + -16 + -8z + -1z2

Reorder the terms:
-16 + -8z + -1z2 = 16 + -16 + 8z + -8z + z2 + -1z2

Combine like terms: 16 + -16 = 0
-16 + -8z + -1z2 = 0 + 8z + -8z + z2 + -1z2
-16 + -8z + -1z2 = 8z + -8z + z2 + -1z2

Combine like terms: 8z + -8z = 0
-16 + -8z + -1z2 = 0 + z2 + -1z2
-16 + -8z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-16 + -8z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 8z + z2) = 0

Factor a trinomial.
-1((4 + z)(4 + z)) = 0

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

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Subproblem 2
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + z = 0 + -4
z = 0 + -4

Combine like terms: 0 + -4 = -4
z = -4

Simplifying
z = -4
Solution
z = {-4, -4}