(x-5)(x+1)(x+3i)=0

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Solution for (x-5)(x+1)(x+3i)=0 equation: 


Simplifying
(x + -5)(x + 1)(x + 3i) = 0

Reorder the terms:
(-5 + x)(x + 1)(x + 3i) = 0

Reorder the terms:
(-5 + x)(1 + x)(x + 3i) = 0

Reorder the terms:
(-5 + x)(1 + x)(3i + x) = 0

Multiply (-5 + x) * (1 + x)
(-5(1 + x) + x(1 + x))(3i + x) = 0
((1 * -5 + x * -5) + x(1 + x))(3i + x) = 0
((-5 + -5x) + x(1 + x))(3i + x) = 0
(-5 + -5x + (1 * x + x * x))(3i + x) = 0
(-5 + -5x + (1x + x2))(3i + x) = 0

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

Multiply (-5 + -4x + x2) * (3i + x)
(-5(3i + x) + -4x * (3i + x) + x2(3i + x)) = 0
((3i * -5 + x * -5) + -4x * (3i + x) + x2(3i + x)) = 0
((-15i + -5x) + -4x * (3i + x) + x2(3i + x)) = 0
(-15i + -5x + (3i * -4x + x * -4x) + x2(3i + x)) = 0
(-15i + -5x + (-12ix + -4x2) + x2(3i + x)) = 0
(-15i + -5x + -12ix + -4x2 + (3i * x2 + x * x2)) = 0
(-15i + -5x + -12ix + -4x2 + (3ix2 + x3)) = 0

Reorder the terms:
(-15i + -12ix + 3ix2 + -5x + -4x2 + x3) = 0
(-15i + -12ix + 3ix2 + -5x + -4x2 + x3) = 0

Solving
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 0

Solving for variable 'i'.

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

Add '5x' to each side of the equation.
-15i + -12ix + 3ix2 + -5x + -4x2 + 5x + x3 = 0 + 5x

Reorder the terms:
-15i + -12ix + 3ix2 + -5x + 5x + -4x2 + x3 = 0 + 5x

Combine like terms: -5x + 5x = 0
-15i + -12ix + 3ix2 + 0 + -4x2 + x3 = 0 + 5x
-15i + -12ix + 3ix2 + -4x2 + x3 = 0 + 5x
Remove the zero:
-15i + -12ix + 3ix2 + -4x2 + x3 = 5x

Add '4x2' to each side of the equation.
-15i + -12ix + 3ix2 + -4x2 + 4x2 + x3 = 5x + 4x2

Combine like terms: -4x2 + 4x2 = 0
-15i + -12ix + 3ix2 + 0 + x3 = 5x + 4x2
-15i + -12ix + 3ix2 + x3 = 5x + 4x2

Add '-1x3' to each side of the equation.
-15i + -12ix + 3ix2 + x3 + -1x3 = 5x + 4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-15i + -12ix + 3ix2 + 0 = 5x + 4x2 + -1x3
-15i + -12ix + 3ix2 = 5x + 4x2 + -1x3

Reorder the terms:
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 5x + -5x + 4x2 + -4x2 + -1x3 + x3

Combine like terms: 5x + -5x = 0
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 0 + 4x2 + -4x2 + -1x3 + x3
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 4x2 + -4x2 + -1x3 + x3

Combine like terms: 4x2 + -4x2 = 0
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 0 + -1x3 + x3
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-15i + -12ix + 3ix2 + -5x + -4x2 + x3 = 0

The solution to this equation could not be determined.

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