0=4z+[(8z)(z)]

Solution for 0=4z+[(8z)(z)] equation:

Simplifying
0 = 4z + [(8z)(z)]

Remove parenthesis around (8z)
0 = 4z + [8z(z)]

Multiply z * z
0 = 4z + [8z2]

Solving
0 = 4z + [8z2]

Solving for variable 'z'.
Remove the zero:
-4z + [-8z2] = 4z + [8z2] + -4z + [-8z2]

Reorder the terms:
-4z + [-8z2] = 4z + -4z + [8z2] + [-8z2]

Combine like terms: 4z + -4z = 0
-4z + [-8z2] = 0 + [8z2] + [-8z2]
-4z + [-8z2] = [8z2] + [-8z2]

Combine like terms: [8z2] + [-8z2] = 0
-4z + [-8z2] = 0

Factor out the Greatest Common Factor (GCF), '-4z'.
-4z(1 + [2z]) = 0

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

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
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 = {0, -0.5}