(3+i)x^2+(-2-6i)x+12=0

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Solution for (3+i)x^2+(-2-6i)x+12=0 equation: 


Simplifying
(3 + i) * x2 + (-2 + -6i) * x + 12 = 0

Reorder the terms for easier multiplication:
x2(3 + i) + (-2 + -6i) * x + 12 = 0
(3 * x2 + i * x2) + (-2 + -6i) * x + 12 = 0

Reorder the terms:
(ix2 + 3x2) + (-2 + -6i) * x + 12 = 0
(ix2 + 3x2) + (-2 + -6i) * x + 12 = 0

Reorder the terms for easier multiplication:
ix2 + 3x2 + x(-2 + -6i) + 12 = 0
ix2 + 3x2 + (-2 * x + -6i * x) + 12 = 0

Reorder the terms:
ix2 + 3x2 + (-6ix + -2x) + 12 = 0
ix2 + 3x2 + (-6ix + -2x) + 12 = 0

Reorder the terms:
12 + -6ix + ix2 + -2x + 3x2 = 0

Solving
12 + -6ix + ix2 + -2x + 3x2 = 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 + -6ix + ix2 + -2x + -12 + 3x2 = 0 + -12

Reorder the terms:
12 + -12 + -6ix + ix2 + -2x + 3x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -6ix + ix2 + -2x + 3x2 = 0 + -12
-6ix + ix2 + -2x + 3x2 = 0 + -12

Combine like terms: 0 + -12 = -12
-6ix + ix2 + -2x + 3x2 = -12

Add '2x' to each side of the equation.
-6ix + ix2 + -2x + 2x + 3x2 = -12 + 2x

Combine like terms: -2x + 2x = 0
-6ix + ix2 + 0 + 3x2 = -12 + 2x
-6ix + ix2 + 3x2 = -12 + 2x

Add '-3x2' to each side of the equation.
-6ix + ix2 + 3x2 + -3x2 = -12 + 2x + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6ix + ix2 + 0 = -12 + 2x + -3x2
-6ix + ix2 = -12 + 2x + -3x2

Reorder the terms:
12 + -6ix + ix2 + -2x + 3x2 = -12 + 2x + -3x2 + 12 + -2x + 3x2

Reorder the terms:
12 + -6ix + ix2 + -2x + 3x2 = -12 + 12 + 2x + -2x + -3x2 + 3x2

Combine like terms: -12 + 12 = 0
12 + -6ix + ix2 + -2x + 3x2 = 0 + 2x + -2x + -3x2 + 3x2
12 + -6ix + ix2 + -2x + 3x2 = 2x + -2x + -3x2 + 3x2

Combine like terms: 2x + -2x = 0
12 + -6ix + ix2 + -2x + 3x2 = 0 + -3x2 + 3x2
12 + -6ix + ix2 + -2x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
12 + -6ix + ix2 + -2x + 3x2 = 0

The solution to this equation could not be determined.

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