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

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


Simplifying
(x + 4)(x + 5i)(x + -5i) = 0

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

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

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

Multiply (4 + x) * (5i + x)
(4(5i + x) + x(5i + x))(-5i + x) = 0
((5i * 4 + x * 4) + x(5i + x))(-5i + x) = 0
((20i + 4x) + x(5i + x))(-5i + x) = 0
(20i + 4x + (5i * x + x * x))(-5i + x) = 0
(20i + 4x + (5ix + x2))(-5i + x) = 0

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

Multiply (20i + 5ix + 4x + x2) * (-5i + x)
(20i * (-5i + x) + 5ix * (-5i + x) + 4x * (-5i + x) + x2(-5i + x)) = 0
((-5i * 20i + x * 20i) + 5ix * (-5i + x) + 4x * (-5i + x) + x2(-5i + x)) = 0

Reorder the terms:
((20ix + -100i2) + 5ix * (-5i + x) + 4x * (-5i + x) + x2(-5i + x)) = 0
((20ix + -100i2) + 5ix * (-5i + x) + 4x * (-5i + x) + x2(-5i + x)) = 0
(20ix + -100i2 + (-5i * 5ix + x * 5ix) + 4x * (-5i + x) + x2(-5i + x)) = 0

Reorder the terms:
(20ix + -100i2 + (5ix2 + -25i2x) + 4x * (-5i + x) + x2(-5i + x)) = 0
(20ix + -100i2 + (5ix2 + -25i2x) + 4x * (-5i + x) + x2(-5i + x)) = 0
(20ix + -100i2 + 5ix2 + -25i2x + (-5i * 4x + x * 4x) + x2(-5i + x)) = 0
(20ix + -100i2 + 5ix2 + -25i2x + (-20ix + 4x2) + x2(-5i + x)) = 0
(20ix + -100i2 + 5ix2 + -25i2x + -20ix + 4x2 + (-5i * x2 + x * x2)) = 0
(20ix + -100i2 + 5ix2 + -25i2x + -20ix + 4x2 + (-5ix2 + x3)) = 0

Reorder the terms:
(20ix + -20ix + 5ix2 + -5ix2 + -100i2 + -25i2x + 4x2 + x3) = 0

Combine like terms: 20ix + -20ix = 0
(0 + 5ix2 + -5ix2 + -100i2 + -25i2x + 4x2 + x3) = 0
(5ix2 + -5ix2 + -100i2 + -25i2x + 4x2 + x3) = 0

Combine like terms: 5ix2 + -5ix2 = 0
(0 + -100i2 + -25i2x + 4x2 + x3) = 0
(-100i2 + -25i2x + 4x2 + x3) = 0

Solving
-100i2 + -25i2x + 4x2 + x3 = 0

Solving for variable 'i'.

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

Add '-4x2' to each side of the equation.
-100i2 + -25i2x + 4x2 + -4x2 + x3 = 0 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-100i2 + -25i2x + 0 + x3 = 0 + -4x2
-100i2 + -25i2x + x3 = 0 + -4x2
Remove the zero:
-100i2 + -25i2x + x3 = -4x2

Add '-1x3' to each side of the equation.
-100i2 + -25i2x + x3 + -1x3 = -4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-100i2 + -25i2x + 0 = -4x2 + -1x3
-100i2 + -25i2x = -4x2 + -1x3

Reorder the terms:
-100i2 + -25i2x + 4x2 + x3 = -4x2 + 4x2 + -1x3 + x3

Combine like terms: -4x2 + 4x2 = 0
-100i2 + -25i2x + 4x2 + x3 = 0 + -1x3 + x3
-100i2 + -25i2x + 4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
-100i2 + -25i2x + 4x2 + x3 = 0

The solution to this equation could not be determined.

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