x^2-(1+2i)x+(3+3i)=0

Solution for x^2-(1+2i)x+(3+3i)=0 equation:

Simplifying
x2 + -1(1 + 2i) * x + (3 + 3i) = 0

Reorder the terms for easier multiplication:
x2 + -1x(1 + 2i) + (3 + 3i) = 0
x2 + (1 * -1x + 2i * -1x) + (3 + 3i) = 0

Reorder the terms:
x2 + (-2ix + -1x) + (3 + 3i) = 0
x2 + (-2ix + -1x) + (3 + 3i) = 0

Remove parenthesis around (3 + 3i)
x2 + -2ix + -1x + 3 + 3i = 0

Reorder the terms:
3 + 3i + -2ix + -1x + x2 = 0

Solving
3 + 3i + -2ix + -1x + x2 = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + 3i + -2ix + -1x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 3i + -2ix + -1x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3i + -2ix + -1x + x2 = 0 + -3
3i + -2ix + -1x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
3i + -2ix + -1x + x2 = -3

Add 'x' to each side of the equation.
3i + -2ix + -1x + x + x2 = -3 + x

Combine like terms: -1x + x = 0
3i + -2ix + 0 + x2 = -3 + x
3i + -2ix + x2 = -3 + x

Add '-1x2' to each side of the equation.
3i + -2ix + x2 + -1x2 = -3 + x + -1x2

Combine like terms: x2 + -1x2 = 0
3i + -2ix + 0 = -3 + x + -1x2
3i + -2ix = -3 + x + -1x2

Reorder the terms:
3 + 3i + -2ix + -1x + x2 = -3 + x + -1x2 + 3 + -1x + x2

Reorder the terms:
3 + 3i + -2ix + -1x + x2 = -3 + 3 + x + -1x + -1x2 + x2

Combine like terms: -3 + 3 = 0
3 + 3i + -2ix + -1x + x2 = 0 + x + -1x + -1x2 + x2
3 + 3i + -2ix + -1x + x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
3 + 3i + -2ix + -1x + x2 = 0 + -1x2 + x2
3 + 3i + -2ix + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3 + 3i + -2ix + -1x + x2 = 0

The solution to this equation could not be determined.