z^4-4z^3+17z^2=0

Solution for z^4-4z^3+17z^2=0 equation:

Simplifying
z4 + -4z3 + 17z2 = 0

Reorder the terms:
17z2 + -4z3 + z4 = 0

Solving
17z2 + -4z3 + z4 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z2'.
z2(17 + -4z + 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 '(17 + -4z + z2)' equal to zero and attempt to solve:

Simplifying
17 + -4z + z2 = 0

Solving
17 + -4z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -4z + -17 + z2 = 0 + -17

Reorder the terms:
17 + -17 + -4z + z2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4z + z2 = 0 + -17
-4z + z2 = 0 + -17

Combine like terms: 0 + -17 = -17
-4z + z2 = -17

The z term is -4z.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4z + 4 + z2 = -17 + 4

Reorder the terms:
4 + -4z + z2 = -17 + 4

Combine like terms: -17 + 4 = -13
4 + -4z + z2 = -13

Factor a perfect square on the left side:
(z + -2)(z + -2) = -13

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}