3z^2+16z+16=0

Solution for 3z^2+16z+16=0 equation:

Simplifying
3z2 + 16z + 16 = 0

Reorder the terms:
16 + 16z + 3z2 = 0

Solving
16 + 16z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(4 + z)(4 + 3z) = 0

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 + 3z)' equal to zero and attempt to solve:

Simplifying
4 + 3z = 0

Solving
4 + 3z = 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 + 3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z = 0 + -4
3z = 0 + -4

Combine like terms: 0 + -4 = -4
3z = -4

Divide each side by '3'.
z = -1.333333333

Simplifying
z = -1.333333333
Solution
z = {-4, -1.333333333}