z^2+(1+i)z+(-6+2i)=0

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Solution for z^2+(1+i)z+(-6+2i)=0 equation: 


Simplifying
z2 + (1 + i) * z + (-6 + 2i) = 0

Reorder the terms for easier multiplication:
z2 + z(1 + i) + (-6 + 2i) = 0
z2 + (1 * z + i * z) + (-6 + 2i) = 0

Reorder the terms:
z2 + (iz + 1z) + (-6 + 2i) = 0
z2 + (iz + 1z) + (-6 + 2i) = 0

Remove parenthesis around (-6 + 2i)
z2 + iz + 1z + -6 + 2i = 0

Reorder the terms:
-6 + 2i + iz + 1z + z2 = 0

Solving
-6 + 2i + iz + 1z + z2 = 0

Solving for variable 'i'.

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

Add '6' to each side of the equation.
-6 + 2i + iz + 1z + 6 + z2 = 0 + 6

Reorder the terms:
-6 + 6 + 2i + iz + 1z + z2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 2i + iz + 1z + z2 = 0 + 6
2i + iz + 1z + z2 = 0 + 6

Combine like terms: 0 + 6 = 6
2i + iz + 1z + z2 = 6

Add '-1z' to each side of the equation.
2i + iz + 1z + -1z + z2 = 6 + -1z

Combine like terms: 1z + -1z = 0
2i + iz + 0 + z2 = 6 + -1z
2i + iz + z2 = 6 + -1z

Add '-1z2' to each side of the equation.
2i + iz + z2 + -1z2 = 6 + -1z + -1z2

Combine like terms: z2 + -1z2 = 0
2i + iz + 0 = 6 + -1z + -1z2
2i + iz = 6 + -1z + -1z2

Reorder the terms:
-6 + 2i + iz + z + z2 = 6 + -1z + -1z2 + -6 + z + z2

Reorder the terms:
-6 + 2i + iz + z + z2 = 6 + -6 + -1z + z + -1z2 + z2

Combine like terms: 6 + -6 = 0
-6 + 2i + iz + z + z2 = 0 + -1z + z + -1z2 + z2
-6 + 2i + iz + z + z2 = -1z + z + -1z2 + z2

Combine like terms: -1z + z = 0
-6 + 2i + iz + z + z2 = 0 + -1z2 + z2
-6 + 2i + iz + z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
-6 + 2i + iz + z + z2 = 0

The solution to this equation could not be determined.

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