x^2+(1+2i)x+(3+4i)=0

Solution for x^2+(1+2i)x+(3+4i)=0 equation:

Simplifying
x2 + (1 + 2i) * x + (3 + 4i) = 0

Reorder the terms for easier multiplication:
x2 + x(1 + 2i) + (3 + 4i) = 0
x2 + (1 * x + 2i * x) + (3 + 4i) = 0

Reorder the terms:
x2 + (2ix + 1x) + (3 + 4i) = 0
x2 + (2ix + 1x) + (3 + 4i) = 0

Remove parenthesis around (3 + 4i)
x2 + 2ix + 1x + 3 + 4i = 0

Reorder the terms:
3 + 4i + 2ix + 1x + x2 = 0

Solving
3 + 4i + 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 + 4i + 2ix + 1x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 4i + 2ix + 1x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i + 2ix + 1x + x2 = 0 + -3
4i + 2ix + 1x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4i + 2ix + 1x + x2 = -3

Add '-1x' to each side of the equation.
4i + 2ix + 1x + -1x + x2 = -3 + -1x

Combine like terms: 1x + -1x = 0
4i + 2ix + 0 + x2 = -3 + -1x
4i + 2ix + x2 = -3 + -1x

Add '-1x2' to each side of the equation.
4i + 2ix + x2 + -1x2 = -3 + -1x + -1x2

Combine like terms: x2 + -1x2 = 0
4i + 2ix + 0 = -3 + -1x + -1x2
4i + 2ix = -3 + -1x + -1x2

Reorder the terms:
3 + 4i + 2ix + x + x2 = -3 + -1x + -1x2 + 3 + x + x2

Reorder the terms:
3 + 4i + 2ix + x + x2 = -3 + 3 + -1x + x + -1x2 + x2

Combine like terms: -3 + 3 = 0
3 + 4i + 2ix + x + x2 = 0 + -1x + x + -1x2 + x2
3 + 4i + 2ix + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
3 + 4i + 2ix + x + x2 = 0 + -1x2 + x2
3 + 4i + 2ix + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
3 + 4i + 2ix + x + x2 = 0

The solution to this equation could not be determined.