(x+5)(x+4+3i)(x+4-3i)=0

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Solution for (x+5)(x+4+3i)(x+4-3i)=0 equation:


Simplifying
(x + 5)(x + 4 + 3i)(x + 4 + -3i) = 0

Reorder the terms:
(5 + x)(x + 4 + 3i)(x + 4 + -3i) = 0

Reorder the terms:
(5 + x)(4 + 3i + x)(x + 4 + -3i) = 0

Reorder the terms:
(5 + x)(4 + 3i + x)(4 + -3i + x) = 0

Multiply (5 + x) * (4 + 3i + x)
(5(4 + 3i + x) + x(4 + 3i + x))(4 + -3i + x) = 0
((4 * 5 + 3i * 5 + x * 5) + x(4 + 3i + x))(4 + -3i + x) = 0
((20 + 15i + 5x) + x(4 + 3i + x))(4 + -3i + x) = 0
(20 + 15i + 5x + (4 * x + 3i * x + x * x))(4 + -3i + x) = 0

Reorder the terms:
(20 + 15i + 5x + (3ix + 4x + x2))(4 + -3i + x) = 0
(20 + 15i + 5x + (3ix + 4x + x2))(4 + -3i + x) = 0

Reorder the terms:
(20 + 15i + 3ix + 5x + 4x + x2)(4 + -3i + x) = 0

Combine like terms: 5x + 4x = 9x
(20 + 15i + 3ix + 9x + x2)(4 + -3i + x) = 0

Multiply (20 + 15i + 3ix + 9x + x2) * (4 + -3i + x)
(20(4 + -3i + x) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
((4 * 20 + -3i * 20 + x * 20) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
((80 + -60i + 20x) + 15i * (4 + -3i + x) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + (4 * 15i + -3i * 15i + x * 15i) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0

Reorder the terms:
(80 + -60i + 20x + (60i + 15ix + -45i2) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + (60i + 15ix + -45i2) + 3ix * (4 + -3i + x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + (4 * 3ix + -3i * 3ix + x * 3ix) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0

Reorder the terms:
(80 + -60i + 20x + 60i + 15ix + -45i2 + (12ix + 3ix2 + -9i2x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + (12ix + 3ix2 + -9i2x) + 9x * (4 + -3i + x) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (4 * 9x + -3i * 9x + x * 9x) + x2(4 + -3i + x)) = 0

Reorder the terms:
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (-27ix + 36x + 9x2) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + (-27ix + 36x + 9x2) + x2(4 + -3i + x)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (4 * x2 + -3i * x2 + x * x2)) = 0

Reorder the terms:
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (-3ix2 + 4x2 + x3)) = 0
(80 + -60i + 20x + 60i + 15ix + -45i2 + 12ix + 3ix2 + -9i2x + -27ix + 36x + 9x2 + (-3ix2 + 4x2 + x3)) = 0

Reorder the terms:
(80 + -60i + 60i + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0

Combine like terms: -60i + 60i = 0
(80 + 0 + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0
(80 + 15ix + 12ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0

Combine like terms: 15ix + 12ix = 27ix
(80 + 27ix + -27ix + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0

Combine like terms: 27ix + -27ix = 0
(80 + 0 + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0
(80 + 3ix2 + -3ix2 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0

Combine like terms: 3ix2 + -3ix2 = 0
(80 + 0 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0
(80 + -45i2 + -9i2x + 20x + 36x + 9x2 + 4x2 + x3) = 0

Combine like terms: 20x + 36x = 56x
(80 + -45i2 + -9i2x + 56x + 9x2 + 4x2 + x3) = 0

Combine like terms: 9x2 + 4x2 = 13x2
(80 + -45i2 + -9i2x + 56x + 13x2 + x3) = 0

Solving
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0

Solving for variable 'i'.

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

Add '-80' to each side of the equation.
80 + -45i2 + -9i2x + 56x + 13x2 + -80 + x3 = 0 + -80

Reorder the terms:
80 + -80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80
-45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -80

Combine like terms: 0 + -80 = -80
-45i2 + -9i2x + 56x + 13x2 + x3 = -80

Add '-56x' to each side of the equation.
-45i2 + -9i2x + 56x + 13x2 + -56x + x3 = -80 + -56x

Reorder the terms:
-45i2 + -9i2x + 56x + -56x + 13x2 + x3 = -80 + -56x

Combine like terms: 56x + -56x = 0
-45i2 + -9i2x + 0 + 13x2 + x3 = -80 + -56x
-45i2 + -9i2x + 13x2 + x3 = -80 + -56x

Add '-13x2' to each side of the equation.
-45i2 + -9i2x + 13x2 + -13x2 + x3 = -80 + -56x + -13x2

Combine like terms: 13x2 + -13x2 = 0
-45i2 + -9i2x + 0 + x3 = -80 + -56x + -13x2
-45i2 + -9i2x + x3 = -80 + -56x + -13x2

Add '-1x3' to each side of the equation.
-45i2 + -9i2x + x3 + -1x3 = -80 + -56x + -13x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-45i2 + -9i2x + 0 = -80 + -56x + -13x2 + -1x3
-45i2 + -9i2x = -80 + -56x + -13x2 + -1x3

Reorder the terms:
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -80 + -56x + -13x2 + -1x3 + 80 + 56x + 13x2 + x3

Reorder the terms:
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -80 + 80 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3

Combine like terms: -80 + 80 = 0
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -56x + 56x + -13x2 + 13x2 + -1x3 + x3
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -56x + 56x + -13x2 + 13x2 + -1x3 + x3

Combine like terms: -56x + 56x = 0
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -13x2 + 13x2 + -1x3 + x3
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -13x2 + 13x2 + -1x3 + x3

Combine like terms: -13x2 + 13x2 = 0
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0 + -1x3 + x3
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
80 + -45i2 + -9i2x + 56x + 13x2 + x3 = 0

The solution to this equation could not be determined.

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