z^3+z^2+35z=0

Solution for z^3+z^2+35z=0 equation:

Simplifying
z3 + z2 + 35z = 0

Reorder the terms:
35z + z2 + z3 = 0

Solving
35z + z2 + z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(35 + z + z2) = 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 '(35 + z + z2)' equal to zero and attempt to solve:

Simplifying
35 + z + z2 = 0

Solving
35 + z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + z + -35 + z2 = 0 + -35

Reorder the terms:
35 + -35 + z + z2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + z + z2 = 0 + -35
z + z2 = 0 + -35

Combine like terms: 0 + -35 = -35
z + z2 = -35

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 = -35 + 0.25

Reorder the terms:
0.25 + z + z2 = -35 + 0.25

Combine like terms: -35 + 0.25 = -34.75
0.25 + z + z2 = -34.75

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -34.75

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}