(4z+2)(4+z)=0

Solution for (4z+2)(4+z)=0 equation:

Simplifying
(4z + 2)(4 + z) = 0

Reorder the terms:
(2 + 4z)(4 + z) = 0

Multiply (2 + 4z) * (4 + z)
(2(4 + z) + 4z * (4 + z)) = 0
((4 * 2 + z * 2) + 4z * (4 + z)) = 0
((8 + 2z) + 4z * (4 + z)) = 0
(8 + 2z + (4 * 4z + z * 4z)) = 0
(8 + 2z + (16z + 4z2)) = 0

Combine like terms: 2z + 16z = 18z
(8 + 18z + 4z2) = 0

Solving
8 + 18z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 9z + 2z2) = 0

Factor a trinomial.
2((4 + z)(1 + 2z)) = 0

Ignore the factor 2.
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 '(1 + 2z)' equal to zero and attempt to solve:

Simplifying
1 + 2z = 0

Solving
1 + 2z = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2z = 0 + -1
2z = 0 + -1

Combine like terms: 0 + -1 = -1
2z = -1

Divide each side by '2'.
z = -0.5

Simplifying
z = -0.5
Solution
z = {-4, -0.5}