0=z-5z^2+10z^3

Solution for 0=z-5z^2+10z^3 equation:

Simplifying
0 = z + -5z2 + 10z3

Solving
0 = z + -5z2 + 10z3

Solving for variable 'z'.
Remove the zero:
-1z + 5z2 + -10z3 = z + -5z2 + 10z3 + -1z + 5z2 + -10z3

Reorder the terms:
-1z + 5z2 + -10z3 = z + -1z + -5z2 + 5z2 + 10z3 + -10z3

Combine like terms: z + -1z = 0
-1z + 5z2 + -10z3 = 0 + -5z2 + 5z2 + 10z3 + -10z3
-1z + 5z2 + -10z3 = -5z2 + 5z2 + 10z3 + -10z3

Combine like terms: -5z2 + 5z2 = 0
-1z + 5z2 + -10z3 = 0 + 10z3 + -10z3
-1z + 5z2 + -10z3 = 10z3 + -10z3

Combine like terms: 10z3 + -10z3 = 0
-1z + 5z2 + -10z3 = 0

Factor out the Greatest Common Factor (GCF), 'z'.
z(-1 + 5z + -10z2) = 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 '(-1 + 5z + -10z2)' equal to zero and attempt to solve:

Simplifying
-1 + 5z + -10z2 = 0

Solving
-1 + 5z + -10z2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
0.1 + -0.5z + z2 = 0

Move the constant term to the right:

Add '-0.1' to each side of the equation.
0.1 + -0.5z + -0.1 + z2 = 0 + -0.1

Reorder the terms:
0.1 + -0.1 + -0.5z + z2 = 0 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + -0.5z + z2 = 0 + -0.1
-0.5z + z2 = 0 + -0.1

Combine like terms: 0 + -0.1 = -0.1
-0.5z + z2 = -0.1

The z term is -0.5z.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5z + 0.0625 + z2 = -0.1 + 0.0625

Reorder the terms:
0.0625 + -0.5z + z2 = -0.1 + 0.0625

Combine like terms: -0.1 + 0.0625 = -0.0375
0.0625 + -0.5z + z2 = -0.0375

Factor a perfect square on the left side:
(z + -0.25)(z + -0.25) = -0.0375

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}