2iz^2+iz-i=0

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

Simplifying
2iz2 + iz + -1i = 0

Reorder the terms:
-1i + iz + 2iz2 = 0

Solving
-1i + iz + 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), 'i'.
i(-1 + z + 2z2) = 0

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

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 '(1 + -2z)' equal to zero and attempt to solve:

Simplifying
1 + -2z = 0

Solving
1 + -2z = 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 + -2z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2z = 0 + -1
-2z = 0 + -1

Combine like terms: 0 + -1 = -1
-2z = -1

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

Combine like terms: -2z + 2z = 0
0 = -1 + 2z

Simplifying
0 = -1 + 2z

The solution to this equation could not be determined.

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