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

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


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

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

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

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

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

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

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

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

Multiply (-12 + -4i + -1ix + 1x + x2) * (-3 + 1i + x)
(-12(-3 + 1i + x) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
((-3 * -12 + 1i * -12 + x * -12) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
((36 + -12i + -12x) + -4i * (-3 + 1i + x) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + (-3 * -4i + 1i * -4i + x * -4i) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y

Reorder the terms:
(36 + -12i + -12x + (12i + -4ix + -4i2) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + (12i + -4ix + -4i2) + -1ix * (-3 + 1i + x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + (-3 * -1ix + 1i * -1ix + x * -1ix) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i2 + (3ix + -1ix2 + -1i2x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + (3ix + -1ix2 + -1i2x) + 1x * (-3 + 1i + x) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + (-3 * 1x + 1i * 1x + x * 1x) + x2(-3 + 1i + x)) = y

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + (1ix + -3x + 1x2) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + (1ix + -3x + 1x2) + x2(-3 + 1i + x)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + 1ix + -3x + 1x2 + (-3 * x2 + 1i * x2 + x * x2)) = y

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + 1ix + -3x + 1x2 + (1ix2 + -3x2 + x3)) = y
(36 + -12i + -12x + 12i + -4ix + -4i2 + 3ix + -1ix2 + -1i2x + 1ix + -3x + 1x2 + (1ix2 + -3x2 + x3)) = y

Reorder the terms:
(36 + -12i + 12i + -4ix + 3ix + 1ix + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y

Combine like terms: -12i + 12i = 0
(36 + 0 + -4ix + 3ix + 1ix + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y
(36 + -4ix + 3ix + 1ix + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y

Combine like terms: -4ix + 3ix = -1ix
(36 + -1ix + 1ix + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y

Combine like terms: -1ix + 1ix = 0
(36 + 0 + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y
(36 + -1ix2 + 1ix2 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y

Combine like terms: -1ix2 + 1ix2 = 0
(36 + 0 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y
(36 + -4i2 + -1i2x + -12x + -3x + 1x2 + -3x2 + x3) = y

Combine like terms: -12x + -3x = -15x
(36 + -4i2 + -1i2x + -15x + 1x2 + -3x2 + x3) = y

Combine like terms: 1x2 + -3x2 = -2x2
(36 + -4i2 + -1i2x + -15x + -2x2 + x3) = y

Solving
36 + -4i2 + -1i2x + -15x + -2x2 + x3 = y

Solving for variable 'i'.

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

Add '-36' to each side of the equation.
36 + -4i2 + -1i2x + -15x + -2x2 + -36 + x3 = -36 + y

Reorder the terms:
36 + -36 + -4i2 + -1i2x + -15x + -2x2 + x3 = -36 + y

Combine like terms: 36 + -36 = 0
0 + -4i2 + -1i2x + -15x + -2x2 + x3 = -36 + y
-4i2 + -1i2x + -15x + -2x2 + x3 = -36 + y

Add '15x' to each side of the equation.
-4i2 + -1i2x + -15x + -2x2 + 15x + x3 = -36 + 15x + y

Reorder the terms:
-4i2 + -1i2x + -15x + 15x + -2x2 + x3 = -36 + 15x + y

Combine like terms: -15x + 15x = 0
-4i2 + -1i2x + 0 + -2x2 + x3 = -36 + 15x + y
-4i2 + -1i2x + -2x2 + x3 = -36 + 15x + y

Add '2x2' to each side of the equation.
-4i2 + -1i2x + -2x2 + 2x2 + x3 = -36 + 15x + 2x2 + y

Combine like terms: -2x2 + 2x2 = 0
-4i2 + -1i2x + 0 + x3 = -36 + 15x + 2x2 + y
-4i2 + -1i2x + x3 = -36 + 15x + 2x2 + y

Add '-1x3' to each side of the equation.
-4i2 + -1i2x + x3 + -1x3 = -36 + 15x + 2x2 + -1x3 + y

Combine like terms: x3 + -1x3 = 0
-4i2 + -1i2x + 0 = -36 + 15x + 2x2 + -1x3 + y
-4i2 + -1i2x = -36 + 15x + 2x2 + -1x3 + y

Reorder the terms:
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = -36 + 15x + 2x2 + -1x3 + y + 36 + -15x + -2x2 + x3 + -1y

Reorder the terms:
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = -36 + 36 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 + y + -1y

Combine like terms: -36 + 36 = 0
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 0 + 15x + -15x + 2x2 + -2x2 + -1x3 + x3 + y + -1y
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 15x + -15x + 2x2 + -2x2 + -1x3 + x3 + y + -1y

Combine like terms: 15x + -15x = 0
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 0 + 2x2 + -2x2 + -1x3 + x3 + y + -1y
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 2x2 + -2x2 + -1x3 + x3 + y + -1y

Combine like terms: 2x2 + -2x2 = 0
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 0 + -1x3 + x3 + y + -1y
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = -1x3 + x3 + y + -1y

Combine like terms: -1x3 + x3 = 0
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 0 + y + -1y
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = y + -1y

Combine like terms: y + -1y = 0
36 + -4i2 + -1i2x + -15x + -2x2 + x3 + -1y = 0

The solution to this equation could not be determined.

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