3*(((z+1)(z-2))(z+2*I))(z-2*I)=0

Simple and best practice solution for 3(((z+1)(z-2))(z+2I))(z-2*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 3(((z+1)(z-2))(z+2I))(z-2*I)=0 equation:

Simplifying
3(((z + 1)(z + -2))(z + 2I))(z + -2I) = 0

Reorder the terms:
3(((1 + z)(z + -2))(z + 2I))(z + -2I) = 0

Reorder the terms:
3(((1 + z)(-2 + z))(z + 2I))(z + -2I) = 0

Multiply (1 + z) * (-2 + z)
3(((1(-2 + z) + z(-2 + z)))(z + 2I))(z + -2I) = 0
3((((-2 * 1 + z * 1) + z(-2 + z)))(z + 2I))(z + -2I) = 0
3((((-2 + 1z) + z(-2 + z)))(z + 2I))(z + -2I) = 0
3(((-2 + 1z + (-2 * z + z * z)))(z + 2I))(z + -2I) = 0
3(((-2 + 1z + (-2z + z²)))(z + 2I))(z + -2I) = 0

Combine like terms: 1z + -2z = -1z
3(((-2 + -1z + z²))(z + 2I))(z + -2I) = 0

Reorder the terms:
3((-2 + -1z + z²)(2I + z))(z + -2I) = 0

Multiply (-2 + -1z + z²) * (2I + z)
3((-2(2I + z) + -1z * (2I + z) + z²(2I + z)))(z + -2I) = 0
3(((2I * -2 + z * -2) + -1z * (2I + z) + z²(2I + z)))(z + -2I) = 0
3(((-4I + -2z) + -1z * (2I + z) + z²(2I + z)))(z + -2I) = 0
3((-4I + -2z + (2I * -1z + z * -1z) + z²(2I + z)))(z + -2I) = 0
3((-4I + -2z + (-2zI + -1z²) + z²(2I + z)))(z + -2I) = 0
3((-4I + -2z + -2zI + -1z² + (2I * z² + z * z²)))(z + -2I) = 0
3((-4I + -2z + -2zI + -1z² + (2z²I + z³)))(z + -2I) = 0
3((-4I + -2z + -2zI + -1z² + 2z²I + z³))(z + -2I) = 0

Reorder the terms:
3(-4I + -2z + -2zI + -1z² + 2z²I + z³)(-2I + z) = 0

Multiply (-4I + -2z + -2zI + -1z² + 2z²I + z³) * (-2I + z)
3(-4I * (-2I + z) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3((-2I * -4I + z * -4I) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3((8I² + -4zI) + -2z * (-2I + z) + -2zI * (-2I + z) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + (-2I * -2z + z * -2z) + -2zI * (-2I + z) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + (4zI + -2z²) + -2zI * (-2I + z) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + (-2I * -2zI + z * -2zI) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + (4zI² + -2z²I) + -1z² * (-2I + z) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + (-2I * -1z² + z * -1z²) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + (2z²I + -1z³) + 2z²I * (-2I + z) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + 2z²I + -1z³ + (-2I * 2z²I + z * 2z²I) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + 2z²I + -1z³ + (-4z²I² + 2z³I) + z³(-2I + z)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + 2z²I + -1z³ + -4z²I² + 2z³I + (-2I * z³ + z * z³)) = 0
3(8I² + -4zI + 4zI + -2z² + 4zI² + -2z²I + 2z²I + -1z³ + -4z²I² + 2z³I + (-2z³I + z⁴)) = 0

Reorder the terms:
3(8I² + -4zI + 4zI + 4zI² + -2z² + -2z²I + 2z²I + -4z²I² + -1z³ + 2z³I + -2z³I + z⁴) = 0

Combine like terms: -4zI + 4zI = 0
3(8I² + 0 + 4zI² + -2z² + -2z²I + 2z²I + -4z²I² + -1z³ + 2z³I + -2z³I + z⁴) = 0
3(8I² + 4zI² + -2z² + -2z²I + 2z²I + -4z²I² + -1z³ + 2z³I + -2z³I + z⁴) = 0

Combine like terms: -2z²I + 2z²I = 0
3(8I² + 4zI² + -2z² + 0 + -4z²I² + -1z³ + 2z³I + -2z³I + z⁴) = 0
3(8I² + 4zI² + -2z² + -4z²I² + -1z³ + 2z³I + -2z³I + z⁴) = 0

Combine like terms: 2z³I + -2z³I = 0
3(8I² + 4zI² + -2z² + -4z²I² + -1z³ + 0 + z⁴) = 0
3(8I² + 4zI² + -2z² + -4z²I² + -1z³ + z⁴) = 0
(8I² * 3 + 4zI² * 3 + -2z² * 3 + -4z²I² * 3 + -1z³ * 3 + z⁴ * 3) = 0
(24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴) = 0

Solving
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 0

Solving for variable 'I'.

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

Add '6z²' to each side of the equation.
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 6z² + 3z⁴ = 0 + 6z²

Reorder the terms:
24I² + 12zI² + -6z² + 6z² + -12z²I² + -3z³ + 3z⁴ = 0 + 6z²

Combine like terms: -6z² + 6z² = 0
24I² + 12zI² + 0 + -12z²I² + -3z³ + 3z⁴ = 0 + 6z²
24I² + 12zI² + -12z²I² + -3z³ + 3z⁴ = 0 + 6z²
Remove the zero:
24I² + 12zI² + -12z²I² + -3z³ + 3z⁴ = 6z²

Add '3z³' to each side of the equation.
24I² + 12zI² + -12z²I² + -3z³ + 3z³ + 3z⁴ = 6z² + 3z³

Combine like terms: -3z³ + 3z³ = 0
24I² + 12zI² + -12z²I² + 0 + 3z⁴ = 6z² + 3z³
24I² + 12zI² + -12z²I² + 3z⁴ = 6z² + 3z³

Add '-3z⁴' to each side of the equation.
24I² + 12zI² + -12z²I² + 3z⁴ + -3z⁴ = 6z² + 3z³ + -3z⁴

Combine like terms: 3z⁴ + -3z⁴ = 0
24I² + 12zI² + -12z²I² + 0 = 6z² + 3z³ + -3z⁴
24I² + 12zI² + -12z²I² = 6z² + 3z³ + -3z⁴

Reorder the terms:
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 6z² + 3z³ + -3z⁴ + -6z² + -3z³ + 3z⁴

Reorder the terms:
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 6z² + -6z² + 3z³ + -3z³ + -3z⁴ + 3z⁴

Combine like terms: 6z² + -6z² = 0
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 0 + 3z³ + -3z³ + -3z⁴ + 3z⁴
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 3z³ + -3z³ + -3z⁴ + 3z⁴

Combine like terms: 3z³ + -3z³ = 0
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 0 + -3z⁴ + 3z⁴
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = -3z⁴ + 3z⁴

Combine like terms: -3z⁴ + 3z⁴ = 0
24I² + 12zI² + -6z² + -12z²I² + -3z³ + 3z⁴ = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8I² + 4zI² + -2z² + -4z²I² + -1z³ + z⁴) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8I² + 4zI² + -2z² + -4z²I² + -1z³ + z⁴)' equal to zero and attempt to solve:

Simplifying
8I² + 4zI² + -2z² + -4z²I² + -1z³ + z⁴ = 0

Solving
8I² + 4zI² + -2z² + -4z²I² + -1z³ + z⁴ = 0

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

Add '2z²' to each side of the equation.
8I² + 4zI² + -2z² + -4z²I² + -1z³ + 2z² + z⁴ = 0 + 2z²

Reorder the terms:
8I² + 4zI² + -2z² + 2z² + -4z²I² + -1z³ + z⁴ = 0 + 2z²

Combine like terms: -2z² + 2z² = 0
8I² + 4zI² + 0 + -4z²I² + -1z³ + z⁴ = 0 + 2z²
8I² + 4zI² + -4z²I² + -1z³ + z⁴ = 0 + 2z²
Remove the zero:
8I² + 4zI² + -4z²I² + -1z³ + z⁴ = 2z²

Add 'z³' to each side of the equation.
8I² + 4zI² + -4z²I² + -1z³ + z³ + z⁴ = 2z² + z³

Combine like terms: -1z³ + z³ = 0
8I² + 4zI² + -4z²I² + 0 + z⁴ = 2z² + z³
8I² + 4zI² + -4z²I² + z⁴ = 2z² + z³

Add '-1z⁴' to each side of the equation.
8I² + 4zI² + -4z²I² + z⁴ + -1z⁴ = 2z² + z³ + -1z⁴

Combine like terms: z⁴ + -1z⁴ = 0
8I² + 4zI² + -4z²I² + 0 = 2z² + z³ + -1z⁴
8I² + 4zI² + -4z²I² = 2z² + z³ + -1z⁴

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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3*(((z+1)(z-2))(z+2*I))(z-2*I)=0

Simple and best practice solution for 3*(((z+1)(z-2))(z+2*I))(z-2*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 3*(((z+1)(z-2))(z+2*I))(z-2*I)=0 equation:

Subproblem 1

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3(((z+1)(z-2))(z+2I))(z-2*I)=0

Simple and best practice solution for 3(((z+1)(z-2))(z+2I))(z-2*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 3(((z+1)(z-2))(z+2I))(z-2*I)=0 equation: