z^2+(4+2i)z+(2-3i)=0

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Solution for z^2+(4+2i)z+(2-3i)=0 equation: 


Simplifying
z2 + (4 + 2i) * z + (2 + -3i) = 0

Reorder the terms for easier multiplication:
z2 + z(4 + 2i) + (2 + -3i) = 0
z2 + (4 * z + 2i * z) + (2 + -3i) = 0

Reorder the terms:
z2 + (2iz + 4z) + (2 + -3i) = 0
z2 + (2iz + 4z) + (2 + -3i) = 0

Remove parenthesis around (2 + -3i)
z2 + 2iz + 4z + 2 + -3i = 0

Reorder the terms:
2 + -3i + 2iz + 4z + z2 = 0

Solving
2 + -3i + 2iz + 4z + z2 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + -3i + 2iz + 4z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + -3i + 2iz + 4z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i + 2iz + 4z + z2 = 0 + -2
-3i + 2iz + 4z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
-3i + 2iz + 4z + z2 = -2

Add '-4z' to each side of the equation.
-3i + 2iz + 4z + -4z + z2 = -2 + -4z

Combine like terms: 4z + -4z = 0
-3i + 2iz + 0 + z2 = -2 + -4z
-3i + 2iz + z2 = -2 + -4z

Add '-1z2' to each side of the equation.
-3i + 2iz + z2 + -1z2 = -2 + -4z + -1z2

Combine like terms: z2 + -1z2 = 0
-3i + 2iz + 0 = -2 + -4z + -1z2
-3i + 2iz = -2 + -4z + -1z2

Reorder the terms:
2 + -3i + 2iz + 4z + z2 = -2 + -4z + -1z2 + 2 + 4z + z2

Reorder the terms:
2 + -3i + 2iz + 4z + z2 = -2 + 2 + -4z + 4z + -1z2 + z2

Combine like terms: -2 + 2 = 0
2 + -3i + 2iz + 4z + z2 = 0 + -4z + 4z + -1z2 + z2
2 + -3i + 2iz + 4z + z2 = -4z + 4z + -1z2 + z2

Combine like terms: -4z + 4z = 0
2 + -3i + 2iz + 4z + z2 = 0 + -1z2 + z2
2 + -3i + 2iz + 4z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
2 + -3i + 2iz + 4z + z2 = 0

The solution to this equation could not be determined.

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