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

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


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

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

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

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

Reorder the terms:
(3 + 3i + 1x + (6ix + 6x + 2x2) + x2(3 + 3i + x)) = 0
(3 + 3i + 1x + (6ix + 6x + 2x2) + x2(3 + 3i + x)) = 0
(3 + 3i + 1x + 6ix + 6x + 2x2 + (3 * x2 + 3i * x2 + x * x2)) = 0

Reorder the terms:
(3 + 3i + 1x + 6ix + 6x + 2x2 + (3ix2 + 3x2 + x3)) = 0
(3 + 3i + 1x + 6ix + 6x + 2x2 + (3ix2 + 3x2 + x3)) = 0

Reorder the terms:
(3 + 3i + 6ix + 3ix2 + 1x + 6x + 2x2 + 3x2 + x3) = 0

Combine like terms: 1x + 6x = 7x
(3 + 3i + 6ix + 3ix2 + 7x + 2x2 + 3x2 + x3) = 0

Combine like terms: 2x2 + 3x2 = 5x2
(3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3) = 0

Solving
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 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 + 6ix + 3ix2 + 7x + 5x2 + -3 + x3 = 0 + -3

Reorder the terms:
3 + -3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -3
3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -3

Combine like terms: 0 + -3 = -3
3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -3

Add '-7x' to each side of the equation.
3i + 6ix + 3ix2 + 7x + 5x2 + -7x + x3 = -3 + -7x

Reorder the terms:
3i + 6ix + 3ix2 + 7x + -7x + 5x2 + x3 = -3 + -7x

Combine like terms: 7x + -7x = 0
3i + 6ix + 3ix2 + 0 + 5x2 + x3 = -3 + -7x
3i + 6ix + 3ix2 + 5x2 + x3 = -3 + -7x

Add '-5x2' to each side of the equation.
3i + 6ix + 3ix2 + 5x2 + -5x2 + x3 = -3 + -7x + -5x2

Combine like terms: 5x2 + -5x2 = 0
3i + 6ix + 3ix2 + 0 + x3 = -3 + -7x + -5x2
3i + 6ix + 3ix2 + x3 = -3 + -7x + -5x2

Add '-1x3' to each side of the equation.
3i + 6ix + 3ix2 + x3 + -1x3 = -3 + -7x + -5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
3i + 6ix + 3ix2 + 0 = -3 + -7x + -5x2 + -1x3
3i + 6ix + 3ix2 = -3 + -7x + -5x2 + -1x3

Reorder the terms:
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -3 + -7x + -5x2 + -1x3 + 3 + 7x + 5x2 + x3

Reorder the terms:
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -3 + 3 + -7x + 7x + -5x2 + 5x2 + -1x3 + x3

Combine like terms: -3 + 3 = 0
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -7x + 7x + -5x2 + 5x2 + -1x3 + x3
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -7x + 7x + -5x2 + 5x2 + -1x3 + x3

Combine like terms: -7x + 7x = 0
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -5x2 + 5x2 + -1x3 + x3
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -5x2 + 5x2 + -1x3 + x3

Combine like terms: -5x2 + 5x2 = 0
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0 + -1x3 + x3
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
3 + 3i + 6ix + 3ix2 + 7x + 5x2 + x3 = 0

The solution to this equation could not be determined.

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