(x-(2+5i))(x-(2-5i))(x+4)=0

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Solution for (x-(2+5i))(x-(2-5i))(x+4)=0 equation: 


Simplifying
(x + -1(2 + 5i))(x + -1(2 + -5i))(x + 4) = 0
(x + (2 * -1 + 5i * -1))(x + -1(2 + -5i))(x + 4) = 0
(x + (-2 + -5i))(x + -1(2 + -5i))(x + 4) = 0

Reorder the terms:
(-2 + -5i + x)(x + -1(2 + -5i))(x + 4) = 0
(-2 + -5i + x)(x + (2 * -1 + -5i * -1))(x + 4) = 0
(-2 + -5i + x)(x + (-2 + 5i))(x + 4) = 0

Reorder the terms:
(-2 + -5i + x)(-2 + 5i + x)(x + 4) = 0

Reorder the terms:
(-2 + -5i + x)(-2 + 5i + x)(4 + x) = 0

Multiply (-2 + -5i + x) * (-2 + 5i + x)
(-2(-2 + 5i + x) + -5i * (-2 + 5i + x) + x(-2 + 5i + x))(4 + x) = 0
((-2 * -2 + 5i * -2 + x * -2) + -5i * (-2 + 5i + x) + x(-2 + 5i + x))(4 + x) = 0
((4 + -10i + -2x) + -5i * (-2 + 5i + x) + x(-2 + 5i + x))(4 + x) = 0
(4 + -10i + -2x + (-2 * -5i + 5i * -5i + x * -5i) + x(-2 + 5i + x))(4 + x) = 0

Reorder the terms:
(4 + -10i + -2x + (10i + -5ix + -25i2) + x(-2 + 5i + x))(4 + x) = 0
(4 + -10i + -2x + (10i + -5ix + -25i2) + x(-2 + 5i + x))(4 + x) = 0
(4 + -10i + -2x + 10i + -5ix + -25i2 + (-2 * x + 5i * x + x * x))(4 + x) = 0

Reorder the terms:
(4 + -10i + -2x + 10i + -5ix + -25i2 + (5ix + -2x + x2))(4 + x) = 0
(4 + -10i + -2x + 10i + -5ix + -25i2 + (5ix + -2x + x2))(4 + x) = 0

Reorder the terms:
(4 + -10i + 10i + -5ix + 5ix + -25i2 + -2x + -2x + x2)(4 + x) = 0

Combine like terms: -10i + 10i = 0
(4 + 0 + -5ix + 5ix + -25i2 + -2x + -2x + x2)(4 + x) = 0
(4 + -5ix + 5ix + -25i2 + -2x + -2x + x2)(4 + x) = 0

Combine like terms: -5ix + 5ix = 0
(4 + 0 + -25i2 + -2x + -2x + x2)(4 + x) = 0
(4 + -25i2 + -2x + -2x + x2)(4 + x) = 0

Combine like terms: -2x + -2x = -4x
(4 + -25i2 + -4x + x2)(4 + x) = 0

Multiply (4 + -25i2 + -4x + x2) * (4 + x)
(4(4 + x) + -25i2 * (4 + x) + -4x * (4 + x) + x2(4 + x)) = 0
((4 * 4 + x * 4) + -25i2 * (4 + x) + -4x * (4 + x) + x2(4 + x)) = 0
((16 + 4x) + -25i2 * (4 + x) + -4x * (4 + x) + x2(4 + x)) = 0
(16 + 4x + (4 * -25i2 + x * -25i2) + -4x * (4 + x) + x2(4 + x)) = 0
(16 + 4x + (-100i2 + -25i2x) + -4x * (4 + x) + x2(4 + x)) = 0
(16 + 4x + -100i2 + -25i2x + (4 * -4x + x * -4x) + x2(4 + x)) = 0
(16 + 4x + -100i2 + -25i2x + (-16x + -4x2) + x2(4 + x)) = 0
(16 + 4x + -100i2 + -25i2x + -16x + -4x2 + (4 * x2 + x * x2)) = 0
(16 + 4x + -100i2 + -25i2x + -16x + -4x2 + (4x2 + x3)) = 0

Reorder the terms:
(16 + -100i2 + -25i2x + 4x + -16x + -4x2 + 4x2 + x3) = 0

Combine like terms: 4x + -16x = -12x
(16 + -100i2 + -25i2x + -12x + -4x2 + 4x2 + x3) = 0

Combine like terms: -4x2 + 4x2 = 0
(16 + -100i2 + -25i2x + -12x + 0 + x3) = 0
(16 + -100i2 + -25i2x + -12x + x3) = 0

Solving
16 + -100i2 + -25i2x + -12x + x3 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -100i2 + -25i2x + -12x + -16 + x3 = 0 + -16

Reorder the terms:
16 + -16 + -100i2 + -25i2x + -12x + x3 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -100i2 + -25i2x + -12x + x3 = 0 + -16
-100i2 + -25i2x + -12x + x3 = 0 + -16

Combine like terms: 0 + -16 = -16
-100i2 + -25i2x + -12x + x3 = -16

Add '12x' to each side of the equation.
-100i2 + -25i2x + -12x + 12x + x3 = -16 + 12x

Combine like terms: -12x + 12x = 0
-100i2 + -25i2x + 0 + x3 = -16 + 12x
-100i2 + -25i2x + x3 = -16 + 12x

Add '-1x3' to each side of the equation.
-100i2 + -25i2x + x3 + -1x3 = -16 + 12x + -1x3

Combine like terms: x3 + -1x3 = 0
-100i2 + -25i2x + 0 = -16 + 12x + -1x3
-100i2 + -25i2x = -16 + 12x + -1x3

Reorder the terms:
16 + -100i2 + -25i2x + -12x + x3 = -16 + 12x + -1x3 + 16 + -12x + x3

Reorder the terms:
16 + -100i2 + -25i2x + -12x + x3 = -16 + 16 + 12x + -12x + -1x3 + x3

Combine like terms: -16 + 16 = 0
16 + -100i2 + -25i2x + -12x + x3 = 0 + 12x + -12x + -1x3 + x3
16 + -100i2 + -25i2x + -12x + x3 = 12x + -12x + -1x3 + x3

Combine like terms: 12x + -12x = 0
16 + -100i2 + -25i2x + -12x + x3 = 0 + -1x3 + x3
16 + -100i2 + -25i2x + -12x + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
16 + -100i2 + -25i2x + -12x + x3 = 0

The solution to this equation could not be determined.

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