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

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


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

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

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

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

Multiply (-3 + x) * (-5 + x)
(-3(-5 + x) + x(-5 + x))(2i + x) = 0
((-5 * -3 + x * -3) + x(-5 + x))(2i + x) = 0
((15 + -3x) + x(-5 + x))(2i + x) = 0
(15 + -3x + (-5 * x + x * x))(2i + x) = 0
(15 + -3x + (-5x + x2))(2i + x) = 0

Combine like terms: -3x + -5x = -8x
(15 + -8x + x2)(2i + x) = 0

Multiply (15 + -8x + x2) * (2i + x)
(15(2i + x) + -8x * (2i + x) + x2(2i + x)) = 0
((2i * 15 + x * 15) + -8x * (2i + x) + x2(2i + x)) = 0
((30i + 15x) + -8x * (2i + x) + x2(2i + x)) = 0
(30i + 15x + (2i * -8x + x * -8x) + x2(2i + x)) = 0
(30i + 15x + (-16ix + -8x2) + x2(2i + x)) = 0
(30i + 15x + -16ix + -8x2 + (2i * x2 + x * x2)) = 0
(30i + 15x + -16ix + -8x2 + (2ix2 + x3)) = 0

Reorder the terms:
(30i + -16ix + 2ix2 + 15x + -8x2 + x3) = 0
(30i + -16ix + 2ix2 + 15x + -8x2 + x3) = 0

Solving
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = 0

Solving for variable 'i'.

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

Add '-15x' to each side of the equation.
30i + -16ix + 2ix2 + 15x + -8x2 + -15x + x3 = 0 + -15x

Reorder the terms:
30i + -16ix + 2ix2 + 15x + -15x + -8x2 + x3 = 0 + -15x

Combine like terms: 15x + -15x = 0
30i + -16ix + 2ix2 + 0 + -8x2 + x3 = 0 + -15x
30i + -16ix + 2ix2 + -8x2 + x3 = 0 + -15x
Remove the zero:
30i + -16ix + 2ix2 + -8x2 + x3 = -15x

Add '8x2' to each side of the equation.
30i + -16ix + 2ix2 + -8x2 + 8x2 + x3 = -15x + 8x2

Combine like terms: -8x2 + 8x2 = 0
30i + -16ix + 2ix2 + 0 + x3 = -15x + 8x2
30i + -16ix + 2ix2 + x3 = -15x + 8x2

Add '-1x3' to each side of the equation.
30i + -16ix + 2ix2 + x3 + -1x3 = -15x + 8x2 + -1x3

Combine like terms: x3 + -1x3 = 0
30i + -16ix + 2ix2 + 0 = -15x + 8x2 + -1x3
30i + -16ix + 2ix2 = -15x + 8x2 + -1x3

Reorder the terms:
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = -15x + 15x + 8x2 + -8x2 + -1x3 + x3

Combine like terms: -15x + 15x = 0
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = 0 + 8x2 + -8x2 + -1x3 + x3
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = 8x2 + -8x2 + -1x3 + x3

Combine like terms: 8x2 + -8x2 = 0
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = 0 + -1x3 + x3
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
30i + -16ix + 2ix2 + 15x + -8x2 + x3 = 0

The solution to this equation could not be determined.

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