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

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


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

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

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

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

Multiply (4 + x) * (-3 + 5i + x)
(4(-3 + 5i + x) + x(-3 + 5i + x))(-3 + -5i + x) = 0
((-3 * 4 + 5i * 4 + x * 4) + x(-3 + 5i + x))(-3 + -5i + x) = 0
((-12 + 20i + 4x) + x(-3 + 5i + x))(-3 + -5i + x) = 0
(-12 + 20i + 4x + (-3 * x + 5i * x + x * x))(-3 + -5i + x) = 0

Reorder the terms:
(-12 + 20i + 4x + (5ix + -3x + x2))(-3 + -5i + x) = 0
(-12 + 20i + 4x + (5ix + -3x + x2))(-3 + -5i + x) = 0

Reorder the terms:
(-12 + 20i + 5ix + 4x + -3x + x2)(-3 + -5i + x) = 0

Combine like terms: 4x + -3x = 1x
(-12 + 20i + 5ix + 1x + x2)(-3 + -5i + x) = 0

Multiply (-12 + 20i + 5ix + 1x + x2) * (-3 + -5i + x)
(-12(-3 + -5i + x) + 20i * (-3 + -5i + x) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
((-3 * -12 + -5i * -12 + x * -12) + 20i * (-3 + -5i + x) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
((36 + 60i + -12x) + 20i * (-3 + -5i + x) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + (-3 * 20i + -5i * 20i + x * 20i) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0

Reorder the terms:
(36 + 60i + -12x + (-60i + 20ix + -100i2) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + (-60i + 20ix + -100i2) + 5ix * (-3 + -5i + x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + (-3 * 5ix + -5i * 5ix + x * 5ix) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0

Reorder the terms:
(36 + 60i + -12x + -60i + 20ix + -100i2 + (-15ix + 5ix2 + -25i2x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + (-15ix + 5ix2 + -25i2x) + 1x * (-3 + -5i + x) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + (-3 * 1x + -5i * 1x + x * 1x) + x2(-3 + -5i + x)) = 0

Reorder the terms:
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + (-5ix + -3x + 1x2) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + (-5ix + -3x + 1x2) + x2(-3 + -5i + x)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + -5ix + -3x + 1x2 + (-3 * x2 + -5i * x2 + x * x2)) = 0

Reorder the terms:
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + -5ix + -3x + 1x2 + (-5ix2 + -3x2 + x3)) = 0
(36 + 60i + -12x + -60i + 20ix + -100i2 + -15ix + 5ix2 + -25i2x + -5ix + -3x + 1x2 + (-5ix2 + -3x2 + x3)) = 0

Reorder the terms:
(36 + 60i + -60i + 20ix + -15ix + -5ix + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0

Combine like terms: 60i + -60i = 0
(36 + 0 + 20ix + -15ix + -5ix + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0
(36 + 20ix + -15ix + -5ix + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0

Combine like terms: 20ix + -15ix = 5ix
(36 + 5ix + -5ix + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0

Combine like terms: 5ix + -5ix = 0
(36 + 0 + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0
(36 + 5ix2 + -5ix2 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0

Combine like terms: 5ix2 + -5ix2 = 0
(36 + 0 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0
(36 + -100i2 + -25i2x + -12x + -3x + 1x2 + -3x2 + x3) = 0

Combine like terms: -12x + -3x = -15x
(36 + -100i2 + -25i2x + -15x + 1x2 + -3x2 + x3) = 0

Combine like terms: 1x2 + -3x2 = -2x2
(36 + -100i2 + -25i2x + -15x + -2x2 + x3) = 0

Solving
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0

Solving for variable 'i'.

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

Add '-36' to each side of the equation.
36 + -100i2 + -25i2x + -15x + -2x2 + -36 + x3 = 0 + -36

Reorder the terms:
36 + -36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0 + -36
-100i2 + -25i2x + -15x + -2x2 + x3 = 0 + -36

Combine like terms: 0 + -36 = -36
-100i2 + -25i2x + -15x + -2x2 + x3 = -36

Add '15x' to each side of the equation.
-100i2 + -25i2x + -15x + -2x2 + 15x + x3 = -36 + 15x

Reorder the terms:
-100i2 + -25i2x + -15x + 15x + -2x2 + x3 = -36 + 15x

Combine like terms: -15x + 15x = 0
-100i2 + -25i2x + 0 + -2x2 + x3 = -36 + 15x
-100i2 + -25i2x + -2x2 + x3 = -36 + 15x

Add '2x2' to each side of the equation.
-100i2 + -25i2x + -2x2 + 2x2 + x3 = -36 + 15x + 2x2

Combine like terms: -2x2 + 2x2 = 0
-100i2 + -25i2x + 0 + x3 = -36 + 15x + 2x2
-100i2 + -25i2x + x3 = -36 + 15x + 2x2

Add '-1x3' to each side of the equation.
-100i2 + -25i2x + x3 + -1x3 = -36 + 15x + 2x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-100i2 + -25i2x + 0 = -36 + 15x + 2x2 + -1x3
-100i2 + -25i2x = -36 + 15x + 2x2 + -1x3

Reorder the terms:
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = -36 + 15x + 2x2 + -1x3 + 36 + -15x + -2x2 + x3

Reorder the terms:
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = -36 + 36 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: -36 + 36 = 0
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 15x + -15x + 2x2 + -2x2 + -1x3 + x3

Combine like terms: 15x + -15x = 0
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0 + 2x2 + -2x2 + -1x3 + x3
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 2x2 + -2x2 + -1x3 + x3

Combine like terms: 2x2 + -2x2 = 0
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0 + -1x3 + x3
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
36 + -100i2 + -25i2x + -15x + -2x2 + x3 = 0

The solution to this equation could not be determined.

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