5z^3+4z^2+2z=

Solution for 5z^3+4z^2+2z= equation:

Simplifying
5z3 + 4z2 + 2z = 0

Reorder the terms:
2z + 4z2 + 5z3 = 0

Solving
2z + 4z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(2 + 4z + 5z2) = 0

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 + 4z + 5z2)' equal to zero and attempt to solve:

Simplifying
2 + 4z + 5z2 = 0

Solving
2 + 4z + 5z2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
0.4 + 0.8z + z2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 0.8z + -0.4 + z2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 0.8z + z2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 0.8z + z2 = 0 + -0.4
0.8z + z2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
0.8z + z2 = -0.4

The z term is 0.8z.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8z + 0.16 + z2 = -0.4 + 0.16

Reorder the terms:
0.16 + 0.8z + z2 = -0.4 + 0.16

Combine like terms: -0.4 + 0.16 = -0.24
0.16 + 0.8z + z2 = -0.24

Factor a perfect square on the left side:
(z + 0.4)(z + 0.4) = -0.24

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}