2iz^2-8iz+6i=0

Solution for 2iz^2-8iz+6i=0 equation:

Simplifying
2iz2 + -8iz + 6i = 0

Reorder the terms:
6i + -8iz + 2iz2 = 0

Solving
6i + -8iz + 2iz2 = 0

Solving for variable 'i'.

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

Factor out the Greatest Common Factor (GCF), '2i'.
2i(3 + -4z + z2) = 0

Factor a trinomial.
2i((1 + -1z)(3 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1z = 0 + -1
-1z = 0 + -1

Combine like terms: 0 + -1 = -1
-1z = -1

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

Combine like terms: -1z + z = 0
0 = -1 + z

Simplifying
0 = -1 + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Add 'z' to each side of the equation.
-1z + z = -3 + z

Combine like terms: -1z + z = 0
0 = -3 + z

Simplifying
0 = -3 + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
i = {0}