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

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

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

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

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

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

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

Multiply (-1ix + 4x) * (-1ix + 4x)
(-1ix * (-1ix + 4x) + 4x * (-1ix + 4x))(ix + 4x)(ix + 4x) = 0
((-1ix * -1ix + 4x * -1ix) + 4x * (-1ix + 4x))(ix + 4x)(ix + 4x) = 0

Reorder the terms:
((-4ix² + 1i²x²) + 4x * (-1ix + 4x))(ix + 4x)(ix + 4x) = 0
((-4ix² + 1i²x²) + 4x * (-1ix + 4x))(ix + 4x)(ix + 4x) = 0
(-4ix² + 1i²x² + (-1ix * 4x + 4x * 4x))(ix + 4x)(ix + 4x) = 0
(-4ix² + 1i²x² + (-4ix² + 16x²))(ix + 4x)(ix + 4x) = 0

Reorder the terms:
(-4ix² + -4ix² + 1i²x² + 16x²)(ix + 4x)(ix + 4x) = 0

Combine like terms: -4ix² + -4ix² = -8ix²
(-8ix² + 1i²x² + 16x²)(ix + 4x)(ix + 4x) = 0

Multiply (-8ix² + 1i²x² + 16x²) * (ix + 4x)
(-8ix² * (ix + 4x) + 1i²x² * (ix + 4x) + 16x² * (ix + 4x))(ix + 4x) = 0
((ix * -8ix² + 4x * -8ix²) + 1i²x² * (ix + 4x) + 16x² * (ix + 4x))(ix + 4x) = 0

Reorder the terms:
((-32ix³ + -8i²x³) + 1i²x² * (ix + 4x) + 16x² * (ix + 4x))(ix + 4x) = 0
((-32ix³ + -8i²x³) + 1i²x² * (ix + 4x) + 16x² * (ix + 4x))(ix + 4x) = 0
(-32ix³ + -8i²x³ + (ix * 1i²x² + 4x * 1i²x²) + 16x² * (ix + 4x))(ix + 4x) = 0

Reorder the terms:
(-32ix³ + -8i²x³ + (4i²x³ + 1i³x³) + 16x² * (ix + 4x))(ix + 4x) = 0
(-32ix³ + -8i²x³ + (4i²x³ + 1i³x³) + 16x² * (ix + 4x))(ix + 4x) = 0
(-32ix³ + -8i²x³ + 4i²x³ + 1i³x³ + (ix * 16x² + 4x * 16x²))(ix + 4x) = 0
(-32ix³ + -8i²x³ + 4i²x³ + 1i³x³ + (16ix³ + 64x³))(ix + 4x) = 0

Reorder the terms:
(-32ix³ + 16ix³ + -8i²x³ + 4i²x³ + 1i³x³ + 64x³)(ix + 4x) = 0

Combine like terms: -32ix³ + 16ix³ = -16ix³
(-16ix³ + -8i²x³ + 4i²x³ + 1i³x³ + 64x³)(ix + 4x) = 0

Combine like terms: -8i²x³ + 4i²x³ = -4i²x³
(-16ix³ + -4i²x³ + 1i³x³ + 64x³)(ix + 4x) = 0

Multiply (-16ix³ + -4i²x³ + 1i³x³ + 64x³) * (ix + 4x)
(-16ix³ * (ix + 4x) + -4i²x³ * (ix + 4x) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0
((ix * -16ix³ + 4x * -16ix³) + -4i²x³ * (ix + 4x) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0

Reorder the terms:
((-64ix⁴ + -16i²x⁴) + -4i²x³ * (ix + 4x) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0
((-64ix⁴ + -16i²x⁴) + -4i²x³ * (ix + 4x) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0
(-64ix⁴ + -16i²x⁴ + (ix * -4i²x³ + 4x * -4i²x³) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0

Reorder the terms:
(-64ix⁴ + -16i²x⁴ + (-16i²x⁴ + -4i³x⁴) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0
(-64ix⁴ + -16i²x⁴ + (-16i²x⁴ + -4i³x⁴) + 1i³x³ * (ix + 4x) + 64x³ * (ix + 4x)) = 0
(-64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + (ix * 1i³x³ + 4x * 1i³x³) + 64x³ * (ix + 4x)) = 0

Reorder the terms:
(-64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + (4i³x⁴ + 1i⁴x⁴) + 64x³ * (ix + 4x)) = 0
(-64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + (4i³x⁴ + 1i⁴x⁴) + 64x³ * (ix + 4x)) = 0
(-64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + (ix * 64x³ + 4x * 64x³)) = 0
(-64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + (64ix⁴ + 256x⁴)) = 0

Reorder the terms:
(-64ix⁴ + 64ix⁴ + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + 256x⁴) = 0

Combine like terms: -64ix⁴ + 64ix⁴ = 0
(0 + -16i²x⁴ + -16i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + 256x⁴) = 0
(-16i²x⁴ + -16i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + 256x⁴) = 0

Combine like terms: -16i²x⁴ + -16i²x⁴ = -32i²x⁴
(-32i²x⁴ + -4i³x⁴ + 4i³x⁴ + 1i⁴x⁴ + 256x⁴) = 0

Combine like terms: -4i³x⁴ + 4i³x⁴ = 0
(-32i²x⁴ + 0 + 1i⁴x⁴ + 256x⁴) = 0
(-32i²x⁴ + 1i⁴x⁴ + 256x⁴) = 0

Solving
-32i²x⁴ + 1i⁴x⁴ + 256x⁴ = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), 'x⁴'.
x⁴(-32i² + i⁴ + 256) = 0

Factor a trinomial.
x⁴((i² + -16)(i² + -16)) = 0

Factor a difference between two squares.
x⁴(((i + 4)(i + -4))(i² + -16)) = 0

Factor a difference between two squares.
x⁴(((i + 4)(i + -4))(i + 4)(i + -4)) = 0

Subproblem 1
Set the factor 'x⁴' equal to zero and attempt to solve:

Simplifying
x⁴ = 0

Solving
x⁴ = 0

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

Add '-1x⁴' to each side of the equation.
x⁴ + -1x⁴ = 0 + -1x⁴
Remove the zero:
0 = -1x⁴

Simplifying
0 = -1x⁴

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2Set the factor '(i + 4)' equal to zero and attempt to solve:

Simplifying
i + 4 = 0

Reorder the terms:
4 + i = 0

Solving
4 + i = 0

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

Add '-4' to each side of the equation.
4 + -4 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
Subproblem 3Set the factor '(i + -4)' equal to zero and attempt to solve:

Simplifying
i + -4 = 0

Reorder the terms:
-4 + i = 0

Solving
-4 + i = 0

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

Add '4' to each side of the equation.
-4 + 4 + i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + i = 0 + 4
i = 0 + 4

Combine like terms: 0 + 4 = 4
i = 4

Simplifying
i = 4
Subproblem 4Set the factor '(i + 4)' equal to zero and attempt to solve:

Simplifying
i + 4 = 0

Reorder the terms:
4 + i = 0

Solving
4 + i = 0

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

Add '-4' to each side of the equation.
4 + -4 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
Subproblem 5Set the factor '(i + -4)' equal to zero and attempt to solve:

Simplifying
i + -4 = 0

Reorder the terms:
-4 + i = 0

Solving
-4 + i = 0

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

Add '4' to each side of the equation.
-4 + 4 + i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + i = 0 + 4
i = 0 + 4

Combine like terms: 0 + 4 = 4
i = 4

Simplifying
i = 4Solution
i = {-4, 4, -4, 4}

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

Simple and best practice solution for (x(4-i))(x(4-i))(x(4+i))(x(4+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-i))(x(4-i))(x(4+i))(x(4+i))=0 equation:

Subproblem 1

Subproblem 2

Subproblem 3

Subproblem 4

Subproblem 5

Solution

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