(x^2+2x+1)(x-2+5i)=

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Solution for (x^2+2x+1)(x-2+5i)= equation: 


Simplifying
(x2 + 2x + 1)(x + -2 + 5i) = 0

Reorder the terms:
(1 + 2x + x2)(x + -2 + 5i) = 0

Reorder the terms:
(1 + 2x + x2)(-2 + 5i + x) = 0

Multiply (1 + 2x + x2) * (-2 + 5i + x)
(1(-2 + 5i + x) + 2x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
((-2 * 1 + 5i * 1 + x * 1) + 2x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
((-2 + 5i + 1x) + 2x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(-2 + 5i + 1x + (-2 * 2x + 5i * 2x + x * 2x) + x2(-2 + 5i + x)) = 0

Reorder the terms:
(-2 + 5i + 1x + (10ix + -4x + 2x2) + x2(-2 + 5i + x)) = 0
(-2 + 5i + 1x + (10ix + -4x + 2x2) + x2(-2 + 5i + x)) = 0
(-2 + 5i + 1x + 10ix + -4x + 2x2 + (-2 * x2 + 5i * x2 + x * x2)) = 0

Reorder the terms:
(-2 + 5i + 1x + 10ix + -4x + 2x2 + (5ix2 + -2x2 + x3)) = 0
(-2 + 5i + 1x + 10ix + -4x + 2x2 + (5ix2 + -2x2 + x3)) = 0

Reorder the terms:
(-2 + 5i + 10ix + 5ix2 + 1x + -4x + 2x2 + -2x2 + x3) = 0

Combine like terms: 1x + -4x = -3x
(-2 + 5i + 10ix + 5ix2 + -3x + 2x2 + -2x2 + x3) = 0

Combine like terms: 2x2 + -2x2 = 0
(-2 + 5i + 10ix + 5ix2 + -3x + 0 + x3) = 0
(-2 + 5i + 10ix + 5ix2 + -3x + x3) = 0

Solving
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 0

Solving for variable 'i'.

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

Add '2' to each side of the equation.
-2 + 5i + 10ix + 5ix2 + -3x + 2 + x3 = 0 + 2

Reorder the terms:
-2 + 2 + 5i + 10ix + 5ix2 + -3x + x3 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5i + 10ix + 5ix2 + -3x + x3 = 0 + 2
5i + 10ix + 5ix2 + -3x + x3 = 0 + 2

Combine like terms: 0 + 2 = 2
5i + 10ix + 5ix2 + -3x + x3 = 2

Add '3x' to each side of the equation.
5i + 10ix + 5ix2 + -3x + 3x + x3 = 2 + 3x

Combine like terms: -3x + 3x = 0
5i + 10ix + 5ix2 + 0 + x3 = 2 + 3x
5i + 10ix + 5ix2 + x3 = 2 + 3x

Add '-1x3' to each side of the equation.
5i + 10ix + 5ix2 + x3 + -1x3 = 2 + 3x + -1x3

Combine like terms: x3 + -1x3 = 0
5i + 10ix + 5ix2 + 0 = 2 + 3x + -1x3
5i + 10ix + 5ix2 = 2 + 3x + -1x3

Reorder the terms:
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 2 + 3x + -1x3 + -2 + -3x + x3

Reorder the terms:
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 2 + -2 + 3x + -3x + -1x3 + x3

Combine like terms: 2 + -2 = 0
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 0 + 3x + -3x + -1x3 + x3
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 3x + -3x + -1x3 + x3

Combine like terms: 3x + -3x = 0
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 0 + -1x3 + x3
-2 + 5i + 10ix + 5ix2 + -3x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-2 + 5i + 10ix + 5ix2 + -3x + x3 = 0

The solution to this equation could not be determined.

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