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

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


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

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

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

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

Multiply (-5 + x) * (-2 + 3i + x)
(-5(-2 + 3i + x) + x(-2 + 3i + x))(-2 + -3i + x) = 0
((-2 * -5 + 3i * -5 + x * -5) + x(-2 + 3i + x))(-2 + -3i + x) = 0
((10 + -15i + -5x) + x(-2 + 3i + x))(-2 + -3i + x) = 0
(10 + -15i + -5x + (-2 * x + 3i * x + x * x))(-2 + -3i + x) = 0

Reorder the terms:
(10 + -15i + -5x + (3ix + -2x + x2))(-2 + -3i + x) = 0
(10 + -15i + -5x + (3ix + -2x + x2))(-2 + -3i + x) = 0

Reorder the terms:
(10 + -15i + 3ix + -5x + -2x + x2)(-2 + -3i + x) = 0

Combine like terms: -5x + -2x = -7x
(10 + -15i + 3ix + -7x + x2)(-2 + -3i + x) = 0

Multiply (10 + -15i + 3ix + -7x + x2) * (-2 + -3i + x)
(10(-2 + -3i + x) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
((-2 * 10 + -3i * 10 + x * 10) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
((-20 + -30i + 10x) + -15i * (-2 + -3i + x) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + (-2 * -15i + -3i * -15i + x * -15i) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0

Reorder the terms:
(-20 + -30i + 10x + (30i + -15ix + 45i2) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + (30i + -15ix + 45i2) + 3ix * (-2 + -3i + x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + (-2 * 3ix + -3i * 3ix + x * 3ix) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0

Reorder the terms:
(-20 + -30i + 10x + 30i + -15ix + 45i2 + (-6ix + 3ix2 + -9i2x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + (-6ix + 3ix2 + -9i2x) + -7x * (-2 + -3i + x) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (-2 * -7x + -3i * -7x + x * -7x) + x2(-2 + -3i + x)) = 0

Reorder the terms:
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (21ix + 14x + -7x2) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + (21ix + 14x + -7x2) + x2(-2 + -3i + x)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-2 * x2 + -3i * x2 + x * x2)) = 0

Reorder the terms:
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-3ix2 + -2x2 + x3)) = 0
(-20 + -30i + 10x + 30i + -15ix + 45i2 + -6ix + 3ix2 + -9i2x + 21ix + 14x + -7x2 + (-3ix2 + -2x2 + x3)) = 0

Reorder the terms:
(-20 + -30i + 30i + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0

Combine like terms: -30i + 30i = 0
(-20 + 0 + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0
(-20 + -15ix + -6ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0

Combine like terms: -15ix + -6ix = -21ix
(-20 + -21ix + 21ix + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0

Combine like terms: -21ix + 21ix = 0
(-20 + 0 + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0
(-20 + 3ix2 + -3ix2 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0

Combine like terms: 3ix2 + -3ix2 = 0
(-20 + 0 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0
(-20 + 45i2 + -9i2x + 10x + 14x + -7x2 + -2x2 + x3) = 0

Combine like terms: 10x + 14x = 24x
(-20 + 45i2 + -9i2x + 24x + -7x2 + -2x2 + x3) = 0

Combine like terms: -7x2 + -2x2 = -9x2
(-20 + 45i2 + -9i2x + 24x + -9x2 + x3) = 0

Solving
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0

Solving for variable 'i'.

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

Add '20' to each side of the equation.
-20 + 45i2 + -9i2x + 24x + -9x2 + 20 + x3 = 0 + 20

Reorder the terms:
-20 + 20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0 + 20
45i2 + -9i2x + 24x + -9x2 + x3 = 0 + 20

Combine like terms: 0 + 20 = 20
45i2 + -9i2x + 24x + -9x2 + x3 = 20

Add '-24x' to each side of the equation.
45i2 + -9i2x + 24x + -9x2 + -24x + x3 = 20 + -24x

Reorder the terms:
45i2 + -9i2x + 24x + -24x + -9x2 + x3 = 20 + -24x

Combine like terms: 24x + -24x = 0
45i2 + -9i2x + 0 + -9x2 + x3 = 20 + -24x
45i2 + -9i2x + -9x2 + x3 = 20 + -24x

Add '9x2' to each side of the equation.
45i2 + -9i2x + -9x2 + 9x2 + x3 = 20 + -24x + 9x2

Combine like terms: -9x2 + 9x2 = 0
45i2 + -9i2x + 0 + x3 = 20 + -24x + 9x2
45i2 + -9i2x + x3 = 20 + -24x + 9x2

Add '-1x3' to each side of the equation.
45i2 + -9i2x + x3 + -1x3 = 20 + -24x + 9x2 + -1x3

Combine like terms: x3 + -1x3 = 0
45i2 + -9i2x + 0 = 20 + -24x + 9x2 + -1x3
45i2 + -9i2x = 20 + -24x + 9x2 + -1x3

Reorder the terms:
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 20 + -24x + 9x2 + -1x3 + -20 + 24x + -9x2 + x3

Reorder the terms:
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 20 + -20 + -24x + 24x + 9x2 + -9x2 + -1x3 + x3

Combine like terms: 20 + -20 = 0
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0 + -24x + 24x + 9x2 + -9x2 + -1x3 + x3
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = -24x + 24x + 9x2 + -9x2 + -1x3 + x3

Combine like terms: -24x + 24x = 0
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0 + 9x2 + -9x2 + -1x3 + x3
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 9x2 + -9x2 + -1x3 + x3

Combine like terms: 9x2 + -9x2 = 0
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0 + -1x3 + x3
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-20 + 45i2 + -9i2x + 24x + -9x2 + x3 = 0

The solution to this equation could not be determined.

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