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

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


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

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

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

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

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

Reorder the terms:
(-5i + ix + -5x + x2)(-1i + x) = 0
(-5i + ix + -5x + x2)(-1i + x) = 0

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

Reorder the terms:
((-5ix + 5i2) + ix(-1i + x) + -5x * (-1i + x) + x2(-1i + x)) = 0
((-5ix + 5i2) + ix(-1i + x) + -5x * (-1i + x) + x2(-1i + x)) = 0
(-5ix + 5i2 + (-1i * ix + x * ix) + -5x * (-1i + x) + x2(-1i + x)) = 0

Reorder the terms:
(-5ix + 5i2 + (ix2 + -1i2x) + -5x * (-1i + x) + x2(-1i + x)) = 0
(-5ix + 5i2 + (ix2 + -1i2x) + -5x * (-1i + x) + x2(-1i + x)) = 0
(-5ix + 5i2 + ix2 + -1i2x + (-1i * -5x + x * -5x) + x2(-1i + x)) = 0
(-5ix + 5i2 + ix2 + -1i2x + (5ix + -5x2) + x2(-1i + x)) = 0
(-5ix + 5i2 + ix2 + -1i2x + 5ix + -5x2 + (-1i * x2 + x * x2)) = 0
(-5ix + 5i2 + ix2 + -1i2x + 5ix + -5x2 + (-1ix2 + x3)) = 0

Reorder the terms:
(-5ix + 5ix + ix2 + -1ix2 + 5i2 + -1i2x + -5x2 + x3) = 0

Combine like terms: -5ix + 5ix = 0
(0 + ix2 + -1ix2 + 5i2 + -1i2x + -5x2 + x3) = 0
(ix2 + -1ix2 + 5i2 + -1i2x + -5x2 + x3) = 0

Combine like terms: ix2 + -1ix2 = 0
(0 + 5i2 + -1i2x + -5x2 + x3) = 0
(5i2 + -1i2x + -5x2 + x3) = 0

Solving
5i2 + -1i2x + -5x2 + x3 = 0

Solving for variable 'i'.

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

Add '5x2' to each side of the equation.
5i2 + -1i2x + -5x2 + 5x2 + x3 = 0 + 5x2

Combine like terms: -5x2 + 5x2 = 0
5i2 + -1i2x + 0 + x3 = 0 + 5x2
5i2 + -1i2x + x3 = 0 + 5x2
Remove the zero:
5i2 + -1i2x + x3 = 5x2

Add '-1x3' to each side of the equation.
5i2 + -1i2x + x3 + -1x3 = 5x2 + -1x3

Combine like terms: x3 + -1x3 = 0
5i2 + -1i2x + 0 = 5x2 + -1x3
5i2 + -1i2x = 5x2 + -1x3

Reorder the terms:
5i2 + -1i2x + -5x2 + x3 = 5x2 + -5x2 + -1x3 + x3

Combine like terms: 5x2 + -5x2 = 0
5i2 + -1i2x + -5x2 + x3 = 0 + -1x3 + x3
5i2 + -1i2x + -5x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
5i2 + -1i2x + -5x2 + x3 = 0

The solution to this equation could not be determined.

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