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

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


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

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

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

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

Multiply (3 + x) * (-2 + -5i + x)
(3(-2 + -5i + x) + x(-2 + -5i + x))(-2 + 5i + x) = 0
((-2 * 3 + -5i * 3 + x * 3) + x(-2 + -5i + x))(-2 + 5i + x) = 0
((-6 + -15i + 3x) + x(-2 + -5i + x))(-2 + 5i + x) = 0
(-6 + -15i + 3x + (-2 * x + -5i * x + x * x))(-2 + 5i + x) = 0

Reorder the terms:
(-6 + -15i + 3x + (-5ix + -2x + x2))(-2 + 5i + x) = 0
(-6 + -15i + 3x + (-5ix + -2x + x2))(-2 + 5i + x) = 0

Reorder the terms:
(-6 + -15i + -5ix + 3x + -2x + x2)(-2 + 5i + x) = 0

Combine like terms: 3x + -2x = 1x
(-6 + -15i + -5ix + 1x + x2)(-2 + 5i + x) = 0

Multiply (-6 + -15i + -5ix + 1x + x2) * (-2 + 5i + x)
(-6(-2 + 5i + x) + -15i * (-2 + 5i + x) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
((-2 * -6 + 5i * -6 + x * -6) + -15i * (-2 + 5i + x) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
((12 + -30i + -6x) + -15i * (-2 + 5i + x) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + (-2 * -15i + 5i * -15i + x * -15i) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0

Reorder the terms:
(12 + -30i + -6x + (30i + -15ix + -75i2) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + (30i + -15ix + -75i2) + -5ix * (-2 + 5i + x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + (-2 * -5ix + 5i * -5ix + x * -5ix) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0

Reorder the terms:
(12 + -30i + -6x + 30i + -15ix + -75i2 + (10ix + -5ix2 + -25i2x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + (10ix + -5ix2 + -25i2x) + 1x * (-2 + 5i + x) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + (-2 * 1x + 5i * 1x + x * 1x) + x2(-2 + 5i + x)) = 0

Reorder the terms:
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + (5ix + -2x + 1x2) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + (5ix + -2x + 1x2) + x2(-2 + 5i + x)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + 5ix + -2x + 1x2 + (-2 * x2 + 5i * x2 + x * x2)) = 0

Reorder the terms:
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + 5ix + -2x + 1x2 + (5ix2 + -2x2 + x3)) = 0
(12 + -30i + -6x + 30i + -15ix + -75i2 + 10ix + -5ix2 + -25i2x + 5ix + -2x + 1x2 + (5ix2 + -2x2 + x3)) = 0

Reorder the terms:
(12 + -30i + 30i + -15ix + 10ix + 5ix + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0

Combine like terms: -30i + 30i = 0
(12 + 0 + -15ix + 10ix + 5ix + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0
(12 + -15ix + 10ix + 5ix + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0

Combine like terms: -15ix + 10ix = -5ix
(12 + -5ix + 5ix + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0

Combine like terms: -5ix + 5ix = 0
(12 + 0 + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0
(12 + -5ix2 + 5ix2 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0

Combine like terms: -5ix2 + 5ix2 = 0
(12 + 0 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0
(12 + -75i2 + -25i2x + -6x + -2x + 1x2 + -2x2 + x3) = 0

Combine like terms: -6x + -2x = -8x
(12 + -75i2 + -25i2x + -8x + 1x2 + -2x2 + x3) = 0

Combine like terms: 1x2 + -2x2 = -1x2
(12 + -75i2 + -25i2x + -8x + -1x2 + x3) = 0

Solving
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0

Solving for variable 'i'.

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

Add '-12' to each side of the equation.
12 + -75i2 + -25i2x + -8x + -1x2 + -12 + x3 = 0 + -12

Reorder the terms:
12 + -12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0 + -12
-75i2 + -25i2x + -8x + -1x2 + x3 = 0 + -12

Combine like terms: 0 + -12 = -12
-75i2 + -25i2x + -8x + -1x2 + x3 = -12

Add '8x' to each side of the equation.
-75i2 + -25i2x + -8x + -1x2 + 8x + x3 = -12 + 8x

Reorder the terms:
-75i2 + -25i2x + -8x + 8x + -1x2 + x3 = -12 + 8x

Combine like terms: -8x + 8x = 0
-75i2 + -25i2x + 0 + -1x2 + x3 = -12 + 8x
-75i2 + -25i2x + -1x2 + x3 = -12 + 8x

Add 'x2' to each side of the equation.
-75i2 + -25i2x + -1x2 + x2 + x3 = -12 + 8x + x2

Combine like terms: -1x2 + x2 = 0
-75i2 + -25i2x + 0 + x3 = -12 + 8x + x2
-75i2 + -25i2x + x3 = -12 + 8x + x2

Add '-1x3' to each side of the equation.
-75i2 + -25i2x + x3 + -1x3 = -12 + 8x + x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-75i2 + -25i2x + 0 = -12 + 8x + x2 + -1x3
-75i2 + -25i2x = -12 + 8x + x2 + -1x3

Reorder the terms:
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = -12 + 8x + x2 + -1x3 + 12 + -8x + -1x2 + x3

Reorder the terms:
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = -12 + 12 + 8x + -8x + x2 + -1x2 + -1x3 + x3

Combine like terms: -12 + 12 = 0
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0 + 8x + -8x + x2 + -1x2 + -1x3 + x3
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 8x + -8x + x2 + -1x2 + -1x3 + x3

Combine like terms: 8x + -8x = 0
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0 + x2 + -1x2 + -1x3 + x3
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = x2 + -1x2 + -1x3 + x3

Combine like terms: x2 + -1x2 = 0
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0 + -1x3 + x3
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
12 + -75i2 + -25i2x + -8x + -1x2 + x3 = 0

The solution to this equation could not be determined.

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