(x^2+(5+3i))(x^2+(5-3i))=0

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Solution for (x^2+(5+3i))(x^2+(5-3i))=0 equation:


Simplifying
(x2 + (5 + 3i))(x2 + (5 + -3i)) = 0

Remove parenthesis around (5 + 3i)
(x2 + 5 + 3i)(x2 + (5 + -3i)) = 0

Reorder the terms:
(5 + 3i + x2)(x2 + (5 + -3i)) = 0

Remove parenthesis around (5 + -3i)
(5 + 3i + x2)(x2 + 5 + -3i) = 0

Reorder the terms:
(5 + 3i + x2)(5 + -3i + x2) = 0

Multiply (5 + 3i + x2) * (5 + -3i + x2)
(5(5 + -3i + x2) + 3i * (5 + -3i + x2) + x2(5 + -3i + x2)) = 0
((5 * 5 + -3i * 5 + x2 * 5) + 3i * (5 + -3i + x2) + x2(5 + -3i + x2)) = 0
((25 + -15i + 5x2) + 3i * (5 + -3i + x2) + x2(5 + -3i + x2)) = 0
(25 + -15i + 5x2 + (5 * 3i + -3i * 3i + x2 * 3i) + x2(5 + -3i + x2)) = 0

Reorder the terms:
(25 + -15i + 5x2 + (15i + 3ix2 + -9i2) + x2(5 + -3i + x2)) = 0
(25 + -15i + 5x2 + (15i + 3ix2 + -9i2) + x2(5 + -3i + x2)) = 0
(25 + -15i + 5x2 + 15i + 3ix2 + -9i2 + (5 * x2 + -3i * x2 + x2 * x2)) = 0

Reorder the terms:
(25 + -15i + 5x2 + 15i + 3ix2 + -9i2 + (-3ix2 + 5x2 + x4)) = 0
(25 + -15i + 5x2 + 15i + 3ix2 + -9i2 + (-3ix2 + 5x2 + x4)) = 0

Reorder the terms:
(25 + -15i + 15i + 3ix2 + -3ix2 + -9i2 + 5x2 + 5x2 + x4) = 0

Combine like terms: -15i + 15i = 0
(25 + 0 + 3ix2 + -3ix2 + -9i2 + 5x2 + 5x2 + x4) = 0
(25 + 3ix2 + -3ix2 + -9i2 + 5x2 + 5x2 + x4) = 0

Combine like terms: 3ix2 + -3ix2 = 0
(25 + 0 + -9i2 + 5x2 + 5x2 + x4) = 0
(25 + -9i2 + 5x2 + 5x2 + x4) = 0

Combine like terms: 5x2 + 5x2 = 10x2
(25 + -9i2 + 10x2 + x4) = 0

Solving
25 + -9i2 + 10x2 + x4 = 0

Solving for variable 'i'.

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

Add '-25' to each side of the equation.
25 + -9i2 + 10x2 + -25 + x4 = 0 + -25

Reorder the terms:
25 + -25 + -9i2 + 10x2 + x4 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -9i2 + 10x2 + x4 = 0 + -25
-9i2 + 10x2 + x4 = 0 + -25

Combine like terms: 0 + -25 = -25
-9i2 + 10x2 + x4 = -25

Add '-10x2' to each side of the equation.
-9i2 + 10x2 + -10x2 + x4 = -25 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-9i2 + 0 + x4 = -25 + -10x2
-9i2 + x4 = -25 + -10x2

Add '-1x4' to each side of the equation.
-9i2 + x4 + -1x4 = -25 + -10x2 + -1x4

Combine like terms: x4 + -1x4 = 0
-9i2 + 0 = -25 + -10x2 + -1x4
-9i2 = -25 + -10x2 + -1x4

Divide each side by '-9'.
i2 = 2.777777778 + 1.111111111x2 + 0.1111111111x4

Simplifying
i2 = 2.777777778 + 1.111111111x2 + 0.1111111111x4

Reorder the terms:
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 2.777777778 + 1.111111111x2 + 0.1111111111x4 + -2.777777778 + -1.111111111x2 + -0.1111111111x4

Reorder the terms:
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 2.777777778 + -2.777777778 + 1.111111111x2 + -1.111111111x2 + 0.1111111111x4 + -0.1111111111x4

Combine like terms: 2.777777778 + -2.777777778 = 0.000000000
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 0.000000000 + 1.111111111x2 + -1.111111111x2 + 0.1111111111x4 + -0.1111111111x4
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 1.111111111x2 + -1.111111111x2 + 0.1111111111x4 + -0.1111111111x4

Combine like terms: 1.111111111x2 + -1.111111111x2 = 0.000000000
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 0.000000000 + 0.1111111111x4 + -0.1111111111x4
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 0.1111111111x4 + -0.1111111111x4

Combine like terms: 0.1111111111x4 + -0.1111111111x4 = 0.0000000000
-2.777777778 + i2 + -1.111111111x2 + -0.1111111111x4 = 0.0000000000

The solution to this equation could not be determined.

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