(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 = 14z
(-8 + 14z + 4z2) = 0

Solving
-8 + 14z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 7z + 2z2) = 0

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

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

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 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 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
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}