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

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

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

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

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

Combine like terms: 16z + 2z = 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}