4z^3+4z^2+8z=

Solution for 4z^3+4z^2+8z= equation:

Simplifying
4z3 + 4z2 + 8z = 0

Reorder the terms:
8z + 4z2 + 4z3 = 0

Solving
8z + 4z2 + 4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(2 + z + z2) = 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 '(2 + z + z2)' equal to zero and attempt to solve:

Simplifying
2 + z + z2 = 0

Solving
2 + z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z + z2 = 0 + -2
z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
z + z2 = -2

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = -2 + 0.25

Reorder the terms:
0.25 + z + z2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + z + z2 = -1.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -1.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
z = {0}