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

Simple and best practice solution for (x+4)(x+1)(x-(3+i))(x-(3-i))=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

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Solution for (x+4)(x+1)(x-(3+i))(x-(3-i))=0 equation:

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

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

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

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

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

Multiply (4 + x) * (1 + x)
(4(1 + x) + x(1 + x))(-3 + -1i + x)(-3 + 1i + x) = 0
((1 * 4 + x * 4) + x(1 + x))(-3 + -1i + x)(-3 + 1i + x) = 0
((4 + 4x) + x(1 + x))(-3 + -1i + x)(-3 + 1i + x) = 0
(4 + 4x + (1 * x + x * x))(-3 + -1i + x)(-3 + 1i + x) = 0
(4 + 4x + (1x + x²))(-3 + -1i + x)(-3 + 1i + x) = 0

Combine like terms: 4x + 1x = 5x
(4 + 5x + x²)(-3 + -1i + x)(-3 + 1i + x) = 0

Multiply (4 + 5x + x²) * (-3 + -1i + x)
(4(-3 + -1i + x) + 5x * (-3 + -1i + x) + x²(-3 + -1i + x))(-3 + 1i + x) = 0
((-3 * 4 + -1i * 4 + x * 4) + 5x * (-3 + -1i + x) + x²(-3 + -1i + x))(-3 + 1i + x) = 0
((-12 + -4i + 4x) + 5x * (-3 + -1i + x) + x²(-3 + -1i + x))(-3 + 1i + x) = 0
(-12 + -4i + 4x + (-3 * 5x + -1i * 5x + x * 5x) + x²(-3 + -1i + x))(-3 + 1i + x) = 0

Reorder the terms:
(-12 + -4i + 4x + (-5ix + -15x + 5x²) + x²(-3 + -1i + x))(-3 + 1i + x) = 0
(-12 + -4i + 4x + (-5ix + -15x + 5x²) + x²(-3 + -1i + x))(-3 + 1i + x) = 0
(-12 + -4i + 4x + -5ix + -15x + 5x² + (-3 * x² + -1i * x² + x * x²))(-3 + 1i + x) = 0

Reorder the terms:
(-12 + -4i + 4x + -5ix + -15x + 5x² + (-1ix² + -3x² + x³))(-3 + 1i + x) = 0
(-12 + -4i + 4x + -5ix + -15x + 5x² + (-1ix² + -3x² + x³))(-3 + 1i + x) = 0

Reorder the terms:
(-12 + -4i + -5ix + -1ix² + 4x + -15x + 5x² + -3x² + x³)(-3 + 1i + x) = 0

Combine like terms: 4x + -15x = -11x
(-12 + -4i + -5ix + -1ix² + -11x + 5x² + -3x² + x³)(-3 + 1i + x) = 0

Combine like terms: 5x² + -3x² = 2x²
(-12 + -4i + -5ix + -1ix² + -11x + 2x² + x³)(-3 + 1i + x) = 0

Multiply (-12 + -4i + -5ix + -1ix² + -11x + 2x² + x³) * (-3 + 1i + x)
(-12(-3 + 1i + x) + -4i * (-3 + 1i + x) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
((-3 * -12 + 1i * -12 + x * -12) + -4i * (-3 + 1i + x) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
((36 + -12i + -12x) + -4i * (-3 + 1i + x) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + (-3 * -4i + 1i * -4i + x * -4i) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0

Reorder the terms:
(36 + -12i + -12x + (12i + -4ix + -4i²) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + (12i + -4ix + -4i²) + -5ix * (-3 + 1i + x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + (-3 * -5ix + 1i * -5ix + x * -5ix) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i² + (15ix + -5ix² + -5i²x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + (15ix + -5ix² + -5i²x) + -1ix² * (-3 + 1i + x) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + (-3 * -1ix² + 1i * -1ix² + x * -1ix²) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + (3ix² + -1ix³ + -1i²x²) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + (3ix² + -1ix³ + -1i²x²) + -11x * (-3 + 1i + x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + (-3 * -11x + 1i * -11x + x * -11x) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + (-11ix + 33x + -11x²) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + (-11ix + 33x + -11x²) + 2x² * (-3 + 1i + x) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + (-3 * 2x² + 1i * 2x² + x * 2x²) + x³(-3 + 1i + x)) = 0

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + (2ix² + -6x² + 2x³) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + (2ix² + -6x² + 2x³) + x³(-3 + 1i + x)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + 2ix² + -6x² + 2x³ + (-3 * x³ + 1i * x³ + x * x³)) = 0

Reorder the terms:
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + 2ix² + -6x² + 2x³ + (1ix³ + -3x³ + x⁴)) = 0
(36 + -12i + -12x + 12i + -4ix + -4i² + 15ix + -5ix² + -5i²x + 3ix² + -1ix³ + -1i²x² + -11ix + 33x + -11x² + 2ix² + -6x² + 2x³ + (1ix³ + -3x³ + x⁴)) = 0

Reorder the terms:
(36 + -12i + 12i + -4ix + 15ix + -11ix + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -12i + 12i = 0
(36 + 0 + -4ix + 15ix + -11ix + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0
(36 + -4ix + 15ix + -11ix + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -4ix + 15ix = 11ix
(36 + 11ix + -11ix + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: 11ix + -11ix = 0
(36 + 0 + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0
(36 + -5ix² + 3ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -5ix² + 3ix² = -2ix²
(36 + -2ix² + 2ix² + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -2ix² + 2ix² = 0
(36 + 0 + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0
(36 + -1ix³ + 1ix³ + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -1ix³ + 1ix³ = 0
(36 + 0 + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0
(36 + -4i² + -5i²x + -1i²x² + -12x + 33x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -12x + 33x = 21x
(36 + -4i² + -5i²x + -1i²x² + 21x + -11x² + -6x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: -11x² + -6x² = -17x²
(36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + 2x³ + -3x³ + x⁴) = 0

Combine like terms: 2x³ + -3x³ = -1x³
(36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴) = 0

Solving
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0

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 + -5i²x + -1i²x² + 21x + -17x² + -1x³ + -36 + x⁴ = 0 + -36

Reorder the terms:
36 + -36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + -36
-4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + -36

Combine like terms: 0 + -36 = -36
-4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = -36

Add '-21x' to each side of the equation.
-4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + -21x + x⁴ = -36 + -21x

Reorder the terms:
-4i² + -5i²x + -1i²x² + 21x + -21x + -17x² + -1x³ + x⁴ = -36 + -21x

Combine like terms: 21x + -21x = 0
-4i² + -5i²x + -1i²x² + 0 + -17x² + -1x³ + x⁴ = -36 + -21x
-4i² + -5i²x + -1i²x² + -17x² + -1x³ + x⁴ = -36 + -21x

Add '17x²' to each side of the equation.
-4i² + -5i²x + -1i²x² + -17x² + -1x³ + 17x² + x⁴ = -36 + -21x + 17x²

Reorder the terms:
-4i² + -5i²x + -1i²x² + -17x² + 17x² + -1x³ + x⁴ = -36 + -21x + 17x²

Combine like terms: -17x² + 17x² = 0
-4i² + -5i²x + -1i²x² + 0 + -1x³ + x⁴ = -36 + -21x + 17x²
-4i² + -5i²x + -1i²x² + -1x³ + x⁴ = -36 + -21x + 17x²

Add 'x³' to each side of the equation.
-4i² + -5i²x + -1i²x² + -1x³ + x³ + x⁴ = -36 + -21x + 17x² + x³

Combine like terms: -1x³ + x³ = 0
-4i² + -5i²x + -1i²x² + 0 + x⁴ = -36 + -21x + 17x² + x³
-4i² + -5i²x + -1i²x² + x⁴ = -36 + -21x + 17x² + x³

Add '-1x⁴' to each side of the equation.
-4i² + -5i²x + -1i²x² + x⁴ + -1x⁴ = -36 + -21x + 17x² + x³ + -1x⁴

Combine like terms: x⁴ + -1x⁴ = 0
-4i² + -5i²x + -1i²x² + 0 = -36 + -21x + 17x² + x³ + -1x⁴
-4i² + -5i²x + -1i²x² = -36 + -21x + 17x² + x³ + -1x⁴

Reorder the terms:
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = -36 + -21x + 17x² + x³ + -1x⁴ + 36 + 21x + -17x² + -1x³ + x⁴

Reorder the terms:
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = -36 + 36 + -21x + 21x + 17x² + -17x² + x³ + -1x³ + -1x⁴ + x⁴

Combine like terms: -36 + 36 = 0
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + -21x + 21x + 17x² + -17x² + x³ + -1x³ + -1x⁴ + x⁴
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = -21x + 21x + 17x² + -17x² + x³ + -1x³ + -1x⁴ + x⁴

Combine like terms: -21x + 21x = 0
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + 17x² + -17x² + x³ + -1x³ + -1x⁴ + x⁴
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 17x² + -17x² + x³ + -1x³ + -1x⁴ + x⁴

Combine like terms: 17x² + -17x² = 0
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + x³ + -1x³ + -1x⁴ + x⁴
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = x³ + -1x³ + -1x⁴ + x⁴

Combine like terms: x³ + -1x³ = 0
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0 + -1x⁴ + x⁴
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = -1x⁴ + x⁴

Combine like terms: -1x⁴ + x⁴ = 0
36 + -4i² + -5i²x + -1i²x² + 21x + -17x² + -1x³ + x⁴ = 0

The solution to this equation could not be determined.

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

Simple and best practice solution for (x+4)(x+1)(x-(3+i))(x-(3-i))=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

Solution for (x+4)(x+1)(x-(3+i))(x-(3-i))=0 equation:

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