(x-5)[x-(4+5i)][x-(4-5i)]=0

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


Simplifying
(x + -5)[x + -1(4 + 5i)][x + -1(4 + -5i)] = 0

Reorder the terms:
(-5 + x)[x + -1(4 + 5i)][x + -1(4 + -5i)] = 0
(-5 + x)[x + (4 * -1 + 5i * -1)][x + -1(4 + -5i)] = 0
(-5 + x)[x + (-4 + -5i)][x + -1(4 + -5i)] = 0

Reorder the terms:
(-5 + x)[-4 + -5i + x][x + -1(4 + -5i)] = 0
(-5 + x)[-4 + -5i + x][x + (4 * -1 + -5i * -1)] = 0
(-5 + x)[-4 + -5i + x][x + (-4 + 5i)] = 0

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

Multiply (-5 + x) * [-4 + -5i + x]
(-5[-4 + -5i + x] + x[-4 + -5i + x])[-4 + 5i + x] = 0
([-4 * -5 + -5i * -5 + x * -5] + x[-4 + -5i + x])[-4 + 5i + x] = 0
([20 + 25i + -5x] + x[-4 + -5i + x])[-4 + 5i + x] = 0
(20 + 25i + -5x + [-4 * x + -5i * x + x * x])[-4 + 5i + x] = 0

Reorder the terms:
(20 + 25i + -5x + [-5ix + -4x + x2])[-4 + 5i + x] = 0
(20 + 25i + -5x + [-5ix + -4x + x2])[-4 + 5i + x] = 0

Reorder the terms:
(20 + 25i + -5ix + -5x + -4x + x2)[-4 + 5i + x] = 0

Combine like terms: -5x + -4x = -9x
(20 + 25i + -5ix + -9x + x2)[-4 + 5i + x] = 0

Multiply (20 + 25i + -5ix + -9x + x2) * [-4 + 5i + x]
(20[-4 + 5i + x] + 25i * [-4 + 5i + x] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
([-4 * 20 + 5i * 20 + x * 20] + 25i * [-4 + 5i + x] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
([-80 + 100i + 20x] + 25i * [-4 + 5i + x] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + [-4 * 25i + 5i * 25i + x * 25i] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0

Reorder the terms:
(-80 + 100i + 20x + [-100i + 25ix + 125i2] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + [-100i + 25ix + 125i2] + -5ix * [-4 + 5i + x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + [-4 * -5ix + 5i * -5ix + x * -5ix] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0

Reorder the terms:
(-80 + 100i + 20x + -100i + 25ix + 125i2 + [20ix + -5ix2 + -25i2x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + [20ix + -5ix2 + -25i2x] + -9x * [-4 + 5i + x] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + [-4 * -9x + 5i * -9x + x * -9x] + x2[-4 + 5i + x]) = 0

Reorder the terms:
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + [-45ix + 36x + -9x2] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + [-45ix + 36x + -9x2] + x2[-4 + 5i + x]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + -45ix + 36x + -9x2 + [-4 * x2 + 5i * x2 + x * x2]) = 0

Reorder the terms:
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + -45ix + 36x + -9x2 + [5ix2 + -4x2 + x3]) = 0
(-80 + 100i + 20x + -100i + 25ix + 125i2 + 20ix + -5ix2 + -25i2x + -45ix + 36x + -9x2 + [5ix2 + -4x2 + x3]) = 0

Reorder the terms:
(-80 + 100i + -100i + 25ix + 20ix + -45ix + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0

Combine like terms: 100i + -100i = 0
(-80 + 0 + 25ix + 20ix + -45ix + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0
(-80 + 25ix + 20ix + -45ix + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0

Combine like terms: 25ix + 20ix = 45ix
(-80 + 45ix + -45ix + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0

Combine like terms: 45ix + -45ix = 0
(-80 + 0 + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0
(-80 + -5ix2 + 5ix2 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0

Combine like terms: -5ix2 + 5ix2 = 0
(-80 + 0 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0
(-80 + 125i2 + -25i2x + 20x + 36x + -9x2 + -4x2 + x3) = 0

Combine like terms: 20x + 36x = 56x
(-80 + 125i2 + -25i2x + 56x + -9x2 + -4x2 + x3) = 0

Combine like terms: -9x2 + -4x2 = -13x2
(-80 + 125i2 + -25i2x + 56x + -13x2 + x3) = 0

Solving
-80 + 125i2 + -25i2x + 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 + 125i2 + -25i2x + 56x + -13x2 + 80 + x3 = 0 + 80

Reorder the terms:
-80 + 80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0 + 80
125i2 + -25i2x + 56x + -13x2 + x3 = 0 + 80

Combine like terms: 0 + 80 = 80
125i2 + -25i2x + 56x + -13x2 + x3 = 80

Add '-56x' to each side of the equation.
125i2 + -25i2x + 56x + -13x2 + -56x + x3 = 80 + -56x

Reorder the terms:
125i2 + -25i2x + 56x + -56x + -13x2 + x3 = 80 + -56x

Combine like terms: 56x + -56x = 0
125i2 + -25i2x + 0 + -13x2 + x3 = 80 + -56x
125i2 + -25i2x + -13x2 + x3 = 80 + -56x

Add '13x2' to each side of the equation.
125i2 + -25i2x + -13x2 + 13x2 + x3 = 80 + -56x + 13x2

Combine like terms: -13x2 + 13x2 = 0
125i2 + -25i2x + 0 + x3 = 80 + -56x + 13x2
125i2 + -25i2x + x3 = 80 + -56x + 13x2

Add '-1x3' to each side of the equation.
125i2 + -25i2x + x3 + -1x3 = 80 + -56x + 13x2 + -1x3

Combine like terms: x3 + -1x3 = 0
125i2 + -25i2x + 0 = 80 + -56x + 13x2 + -1x3
125i2 + -25i2x = 80 + -56x + 13x2 + -1x3

Reorder the terms:
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 80 + -56x + 13x2 + -1x3 + -80 + 56x + -13x2 + x3

Reorder the terms:
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 80 + -80 + -56x + 56x + 13x2 + -13x2 + -1x3 + x3

Combine like terms: 80 + -80 = 0
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0 + -56x + 56x + 13x2 + -13x2 + -1x3 + x3
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = -56x + 56x + 13x2 + -13x2 + -1x3 + x3

Combine like terms: -56x + 56x = 0
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0 + 13x2 + -13x2 + -1x3 + x3
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 13x2 + -13x2 + -1x3 + x3

Combine like terms: 13x2 + -13x2 = 0
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0 + -1x3 + x3
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-80 + 125i2 + -25i2x + 56x + -13x2 + x3 = 0

The solution to this equation could not be determined.

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