z^2+(3-3i)z+(12-i)=0

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Solution for z^2+(3-3i)z+(12-i)=0 equation: 


Simplifying
z2 + (3 + -3i) * z + (12 + -1i) = 0

Reorder the terms for easier multiplication:
z2 + z(3 + -3i) + (12 + -1i) = 0
z2 + (3 * z + -3i * z) + (12 + -1i) = 0

Reorder the terms:
z2 + (-3iz + 3z) + (12 + -1i) = 0
z2 + (-3iz + 3z) + (12 + -1i) = 0

Remove parenthesis around (12 + -1i)
z2 + -3iz + 3z + 12 + -1i = 0

Reorder the terms:
12 + -1i + -3iz + 3z + z2 = 0

Solving
12 + -1i + -3iz + 3z + z2 = 0

Solving for variable 'i'.

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

Add '-12' to each side of the equation.
12 + -1i + -3iz + 3z + -12 + z2 = 0 + -12

Reorder the terms:
12 + -12 + -1i + -3iz + 3z + z2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1i + -3iz + 3z + z2 = 0 + -12
-1i + -3iz + 3z + z2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1i + -3iz + 3z + z2 = -12

Add '-3z' to each side of the equation.
-1i + -3iz + 3z + -3z + z2 = -12 + -3z

Combine like terms: 3z + -3z = 0
-1i + -3iz + 0 + z2 = -12 + -3z
-1i + -3iz + z2 = -12 + -3z

Add '-1z2' to each side of the equation.
-1i + -3iz + z2 + -1z2 = -12 + -3z + -1z2

Combine like terms: z2 + -1z2 = 0
-1i + -3iz + 0 = -12 + -3z + -1z2
-1i + -3iz = -12 + -3z + -1z2

Reorder the terms:
12 + -1i + -3iz + 3z + z2 = -12 + -3z + -1z2 + 12 + 3z + z2

Reorder the terms:
12 + -1i + -3iz + 3z + z2 = -12 + 12 + -3z + 3z + -1z2 + z2

Combine like terms: -12 + 12 = 0
12 + -1i + -3iz + 3z + z2 = 0 + -3z + 3z + -1z2 + z2
12 + -1i + -3iz + 3z + z2 = -3z + 3z + -1z2 + z2

Combine like terms: -3z + 3z = 0
12 + -1i + -3iz + 3z + z2 = 0 + -1z2 + z2
12 + -1i + -3iz + 3z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
12 + -1i + -3iz + 3z + z2 = 0

The solution to this equation could not be determined.

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