(x+3)(x-(-4+i))(x-(4-i))=0

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Solution for (x+3)(x-(-4+i))(x-(4-i))=0 equation: 


Simplifying
(x + 3)(x + -1(-4 + i))(x + -1(4 + -1i)) = 0

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

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

Reorder the terms:
(3 + x)(4 + -1i + x)(-4 + 1i + x) = 0

Multiply (3 + x) * (4 + -1i + x)
(3(4 + -1i + x) + x(4 + -1i + x))(-4 + 1i + x) = 0
((4 * 3 + -1i * 3 + x * 3) + x(4 + -1i + x))(-4 + 1i + x) = 0
((12 + -3i + 3x) + x(4 + -1i + x))(-4 + 1i + x) = 0
(12 + -3i + 3x + (4 * x + -1i * x + x * x))(-4 + 1i + x) = 0

Reorder the terms:
(12 + -3i + 3x + (-1ix + 4x + x2))(-4 + 1i + x) = 0
(12 + -3i + 3x + (-1ix + 4x + x2))(-4 + 1i + x) = 0

Reorder the terms:
(12 + -3i + -1ix + 3x + 4x + x2)(-4 + 1i + x) = 0

Combine like terms: 3x + 4x = 7x
(12 + -3i + -1ix + 7x + x2)(-4 + 1i + x) = 0

Multiply (12 + -3i + -1ix + 7x + x2) * (-4 + 1i + x)
(12(-4 + 1i + x) + -3i * (-4 + 1i + x) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
((-4 * 12 + 1i * 12 + x * 12) + -3i * (-4 + 1i + x) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
((-48 + 12i + 12x) + -3i * (-4 + 1i + x) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + (-4 * -3i + 1i * -3i + x * -3i) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0

Reorder the terms:
(-48 + 12i + 12x + (12i + -3ix + -3i2) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + (12i + -3ix + -3i2) + -1ix * (-4 + 1i + x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + (-4 * -1ix + 1i * -1ix + x * -1ix) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0

Reorder the terms:
(-48 + 12i + 12x + 12i + -3ix + -3i2 + (4ix + -1ix2 + -1i2x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + (4ix + -1ix2 + -1i2x) + 7x * (-4 + 1i + x) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + (-4 * 7x + 1i * 7x + x * 7x) + x2(-4 + 1i + x)) = 0

Reorder the terms:
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + (7ix + -28x + 7x2) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + (7ix + -28x + 7x2) + x2(-4 + 1i + x)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + 7ix + -28x + 7x2 + (-4 * x2 + 1i * x2 + x * x2)) = 0

Reorder the terms:
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + 7ix + -28x + 7x2 + (1ix2 + -4x2 + x3)) = 0
(-48 + 12i + 12x + 12i + -3ix + -3i2 + 4ix + -1ix2 + -1i2x + 7ix + -28x + 7x2 + (1ix2 + -4x2 + x3)) = 0

Reorder the terms:
(-48 + 12i + 12i + -3ix + 4ix + 7ix + -1ix2 + 1ix2 + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0

Combine like terms: 12i + 12i = 24i
(-48 + 24i + -3ix + 4ix + 7ix + -1ix2 + 1ix2 + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0

Combine like terms: -3ix + 4ix = 1ix
(-48 + 24i + 1ix + 7ix + -1ix2 + 1ix2 + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0

Combine like terms: 1ix + 7ix = 8ix
(-48 + 24i + 8ix + -1ix2 + 1ix2 + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0

Combine like terms: -1ix2 + 1ix2 = 0
(-48 + 24i + 8ix + 0 + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0
(-48 + 24i + 8ix + -3i2 + -1i2x + 12x + -28x + 7x2 + -4x2 + x3) = 0

Combine like terms: 12x + -28x = -16x
(-48 + 24i + 8ix + -3i2 + -1i2x + -16x + 7x2 + -4x2 + x3) = 0

Combine like terms: 7x2 + -4x2 = 3x2
(-48 + 24i + 8ix + -3i2 + -1i2x + -16x + 3x2 + x3) = 0

Solving
-48 + 24i + 8ix + -3i2 + -1i2x + -16x + 3x2 + x3 = 0

Solving for variable 'i'.

The solution to this equation could not be determined.

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