(x+2)(x-5)(x-(3+2i))(x-(3-2i))=0

Simple and best practice solution for (x+2)(x-5)(x-(3+2i))(x-(3-2i))=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+2)(x-5)(x-(3+2i))(x-(3-2i))=0 equation:

Simplifying
(x + 2)(x + -5)(x + -1(3 + 2i))(x + -1(3 + -2i)) = 0

Reorder the terms:
(2 + x)(x + -5)(x + -1(3 + 2i))(x + -1(3 + -2i)) = 0

Reorder the terms:
(2 + x)(-5 + x)(x + -1(3 + 2i))(x + -1(3 + -2i)) = 0
(2 + x)(-5 + x)(x + (3 * -1 + 2i * -1))(x + -1(3 + -2i)) = 0
(2 + x)(-5 + x)(x + (-3 + -2i))(x + -1(3 + -2i)) = 0

Reorder the terms:
(2 + x)(-5 + x)(-3 + -2i + x)(x + -1(3 + -2i)) = 0
(2 + x)(-5 + x)(-3 + -2i + x)(x + (3 * -1 + -2i * -1)) = 0
(2 + x)(-5 + x)(-3 + -2i + x)(x + (-3 + 2i)) = 0

Reorder the terms:
(2 + x)(-5 + x)(-3 + -2i + x)(-3 + 2i + x) = 0

Multiply (2 + x) * (-5 + x)
(2(-5 + x) + x(-5 + x))(-3 + -2i + x)(-3 + 2i + x) = 0
((-5 * 2 + x * 2) + x(-5 + x))(-3 + -2i + x)(-3 + 2i + x) = 0
((-10 + 2x) + x(-5 + x))(-3 + -2i + x)(-3 + 2i + x) = 0
(-10 + 2x + (-5 * x + x * x))(-3 + -2i + x)(-3 + 2i + x) = 0
(-10 + 2x + (-5x + x²))(-3 + -2i + x)(-3 + 2i + x) = 0

Combine like terms: 2x + -5x = -3x
(-10 + -3x + x²)(-3 + -2i + x)(-3 + 2i + x) = 0

Multiply (-10 + -3x + x²) * (-3 + -2i + x)
(-10(-3 + -2i + x) + -3x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x) = 0
((-3 * -10 + -2i * -10 + x * -10) + -3x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x) = 0
((30 + 20i + -10x) + -3x * (-3 + -2i + x) + x²(-3 + -2i + x))(-3 + 2i + x) = 0
(30 + 20i + -10x + (-3 * -3x + -2i * -3x + x * -3x) + x²(-3 + -2i + x))(-3 + 2i + x) = 0

Reorder the terms:
(30 + 20i + -10x + (6ix + 9x + -3x²) + x²(-3 + -2i + x))(-3 + 2i + x) = 0
(30 + 20i + -10x + (6ix + 9x + -3x²) + x²(-3 + -2i + x))(-3 + 2i + x) = 0
(30 + 20i + -10x + 6ix + 9x + -3x² + (-3 * x² + -2i * x² + x * x²))(-3 + 2i + x) = 0

Reorder the terms:
(30 + 20i + -10x + 6ix + 9x + -3x² + (-2ix² + -3x² + x³))(-3 + 2i + x) = 0
(30 + 20i + -10x + 6ix + 9x + -3x² + (-2ix² + -3x² + x³))(-3 + 2i + x) = 0

Reorder the terms:
(30 + 20i + 6ix + -2ix² + -10x + 9x + -3x² + -3x² + x³)(-3 + 2i + x) = 0

Combine like terms: -10x + 9x = -1x
(30 + 20i + 6ix + -2ix² + -1x + -3x² + -3x² + x³)(-3 + 2i + x) = 0

Combine like terms: -3x² + -3x² = -6x²
(30 + 20i + 6ix + -2ix² + -1x + -6x² + x³)(-3 + 2i + x) = 0

Multiply (30 + 20i + 6ix + -2ix² + -1x + -6x² + x³) * (-3 + 2i + x)
(30(-3 + 2i + x) + 20i * (-3 + 2i + x) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
((-3 * 30 + 2i * 30 + x * 30) + 20i * (-3 + 2i + x) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
((-90 + 60i + 30x) + 20i * (-3 + 2i + x) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + (-3 * 20i + 2i * 20i + x * 20i) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0

Reorder the terms:
(-90 + 60i + 30x + (-60i + 20ix + 40i²) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + (-60i + 20ix + 40i²) + 6ix * (-3 + 2i + x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + (-3 * 6ix + 2i * 6ix + x * 6ix) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0

Reorder the terms:
(-90 + 60i + 30x + -60i + 20ix + 40i² + (-18ix + 6ix² + 12i²x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + (-18ix + 6ix² + 12i²x) + -2ix² * (-3 + 2i + x) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + (-3 * -2ix² + 2i * -2ix² + x * -2ix²) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0

Reorder the terms:
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + (6ix² + -2ix³ + -4i²x²) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + (6ix² + -2ix³ + -4i²x²) + -1x * (-3 + 2i + x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + (-3 * -1x + 2i * -1x + x * -1x) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0

Reorder the terms:
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + (-2ix + 3x + -1x²) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + (-2ix + 3x + -1x²) + -6x² * (-3 + 2i + x) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + (-3 * -6x² + 2i * -6x² + x * -6x²) + x³(-3 + 2i + x)) = 0

Reorder the terms:
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + (-12ix² + 18x² + -6x³) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + (-12ix² + 18x² + -6x³) + x³(-3 + 2i + x)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + -12ix² + 18x² + -6x³ + (-3 * x³ + 2i * x³ + x * x³)) = 0

Reorder the terms:
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + -12ix² + 18x² + -6x³ + (2ix³ + -3x³ + x⁴)) = 0
(-90 + 60i + 30x + -60i + 20ix + 40i² + -18ix + 6ix² + 12i²x + 6ix² + -2ix³ + -4i²x² + -2ix + 3x + -1x² + -12ix² + 18x² + -6x³ + (2ix³ + -3x³ + x⁴)) = 0

Reorder the terms:
(-90 + 60i + -60i + 20ix + -18ix + -2ix + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 60i + -60i = 0
(-90 + 0 + 20ix + -18ix + -2ix + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0
(-90 + 20ix + -18ix + -2ix + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 20ix + -18ix = 2ix
(-90 + 2ix + -2ix + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 2ix + -2ix = 0
(-90 + 0 + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0
(-90 + 6ix² + 6ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 6ix² + 6ix² = 12ix²
(-90 + 12ix² + -12ix² + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 12ix² + -12ix² = 0
(-90 + 0 + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0
(-90 + -2ix³ + 2ix³ + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: -2ix³ + 2ix³ = 0
(-90 + 0 + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0
(-90 + 40i² + 12i²x + -4i²x² + 30x + 3x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: 30x + 3x = 33x
(-90 + 40i² + 12i²x + -4i²x² + 33x + -1x² + 18x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: -1x² + 18x² = 17x²
(-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -6x³ + -3x³ + x⁴) = 0

Combine like terms: -6x³ + -3x³ = -9x³
(-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴) = 0

Solving
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0

Solving for variable 'i'.

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

Add '90' to each side of the equation.
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + 90 + x⁴ = 0 + 90

Reorder the terms:
-90 + 90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + 90
40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + 90

Combine like terms: 0 + 90 = 90
40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 90

Add '-33x' to each side of the equation.
40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + -33x + x⁴ = 90 + -33x

Reorder the terms:
40i² + 12i²x + -4i²x² + 33x + -33x + 17x² + -9x³ + x⁴ = 90 + -33x

Combine like terms: 33x + -33x = 0
40i² + 12i²x + -4i²x² + 0 + 17x² + -9x³ + x⁴ = 90 + -33x
40i² + 12i²x + -4i²x² + 17x² + -9x³ + x⁴ = 90 + -33x

Add '-17x²' to each side of the equation.
40i² + 12i²x + -4i²x² + 17x² + -9x³ + -17x² + x⁴ = 90 + -33x + -17x²

Reorder the terms:
40i² + 12i²x + -4i²x² + 17x² + -17x² + -9x³ + x⁴ = 90 + -33x + -17x²

Combine like terms: 17x² + -17x² = 0
40i² + 12i²x + -4i²x² + 0 + -9x³ + x⁴ = 90 + -33x + -17x²
40i² + 12i²x + -4i²x² + -9x³ + x⁴ = 90 + -33x + -17x²

Add '9x³' to each side of the equation.
40i² + 12i²x + -4i²x² + -9x³ + 9x³ + x⁴ = 90 + -33x + -17x² + 9x³

Combine like terms: -9x³ + 9x³ = 0
40i² + 12i²x + -4i²x² + 0 + x⁴ = 90 + -33x + -17x² + 9x³
40i² + 12i²x + -4i²x² + x⁴ = 90 + -33x + -17x² + 9x³

Add '-1x⁴' to each side of the equation.
40i² + 12i²x + -4i²x² + x⁴ + -1x⁴ = 90 + -33x + -17x² + 9x³ + -1x⁴

Combine like terms: x⁴ + -1x⁴ = 0
40i² + 12i²x + -4i²x² + 0 = 90 + -33x + -17x² + 9x³ + -1x⁴
40i² + 12i²x + -4i²x² = 90 + -33x + -17x² + 9x³ + -1x⁴

Reorder the terms:
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 90 + -33x + -17x² + 9x³ + -1x⁴ + -90 + 33x + 17x² + -9x³ + x⁴

Reorder the terms:
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 90 + -90 + -33x + 33x + -17x² + 17x² + 9x³ + -9x³ + -1x⁴ + x⁴

Combine like terms: 90 + -90 = 0
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + -33x + 33x + -17x² + 17x² + 9x³ + -9x³ + -1x⁴ + x⁴
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = -33x + 33x + -17x² + 17x² + 9x³ + -9x³ + -1x⁴ + x⁴

Combine like terms: -33x + 33x = 0
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + -17x² + 17x² + 9x³ + -9x³ + -1x⁴ + x⁴
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = -17x² + 17x² + 9x³ + -9x³ + -1x⁴ + x⁴

Combine like terms: -17x² + 17x² = 0
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + 9x³ + -9x³ + -1x⁴ + x⁴
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 9x³ + -9x³ + -1x⁴ + x⁴

Combine like terms: 9x³ + -9x³ = 0
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0 + -1x⁴ + x⁴
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = -1x⁴ + x⁴

Combine like terms: -1x⁴ + x⁴ = 0
-90 + 40i² + 12i²x + -4i²x² + 33x + 17x² + -9x³ + x⁴ = 0

The solution to this equation could not be determined.

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(x+2)(x-5)(x-(3+2i))(x-(3-2i))=0

Simple and best practice solution for (x+2)(x-5)(x-(3+2i))(x-(3-2i))=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+2)(x-5)(x-(3+2i))(x-(3-2i))=0 equation:

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