z^4-2z^3+10z^2=0

Solution for z^4-2z^3+10z^2=0 equation:

Simplifying
z4 + -2z3 + 10z2 = 0

Reorder the terms:
10z2 + -2z3 + z4 = 0

Solving
10z2 + -2z3 + z4 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

Move all terms containing z to the left, all other terms to the right.

Simplifying
z2 = 0

Take the square root of each side:
z = {0}
Subproblem 2
Set the factor '(10 + -2z + z2)' equal to zero and attempt to solve:

Simplifying
10 + -2z + z2 = 0

Solving
10 + -2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -2z + -10 + z2 = 0 + -10

Reorder the terms:
10 + -10 + -2z + z2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -2z + z2 = 0 + -10
-2z + z2 = 0 + -10

Combine like terms: 0 + -10 = -10
-2z + z2 = -10

The z term is -2z.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2z + 1 + z2 = -10 + 1

Reorder the terms:
1 + -2z + z2 = -10 + 1

Combine like terms: -10 + 1 = -9
1 + -2z + z2 = -9

Factor a perfect square on the left side:
(z + -1)(z + -1) = -9

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}