2z^3+20z^2=-82z

Solution for 2z^3+20z^2=-82z equation:

Simplifying
2z3 + 20z2 = -82z

Reorder the terms:
20z2 + 2z3 = -82z

Solving
20z2 + 2z3 = -82z

Solving for variable 'z'.

Reorder the terms:
82z + 20z2 + 2z3 = -82z + 82z

Combine like terms: -82z + 82z = 0
82z + 20z2 + 2z3 = 0

Factor out the Greatest Common Factor (GCF), '2z'.
2z(41 + 10z + z2) = 0

Ignore the factor 2.
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 '(41 + 10z + z2)' equal to zero and attempt to solve:

Simplifying
41 + 10z + z2 = 0

Solving
41 + 10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 10z + -41 + z2 = 0 + -41

Reorder the terms:
41 + -41 + 10z + z2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 10z + z2 = 0 + -41
10z + z2 = 0 + -41

Combine like terms: 0 + -41 = -41
10z + z2 = -41

The z term is 10z.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10z + 25 + z2 = -41 + 25

Reorder the terms:
25 + 10z + z2 = -41 + 25

Combine like terms: -41 + 25 = -16
25 + 10z + z2 = -16

Factor a perfect square on the left side:
(z + 5)(z + 5) = -16

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}