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

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Solution for (x+5)(2+3i)(2-3i)=0 equation: 


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

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

Multiply (5 + x) * (2 + 3i)
(5(2 + 3i) + x(2 + 3i))(2 + -3i) = 0
((2 * 5 + 3i * 5) + x(2 + 3i))(2 + -3i) = 0
((10 + 15i) + x(2 + 3i))(2 + -3i) = 0
(10 + 15i + (2 * x + 3i * x))(2 + -3i) = 0

Reorder the terms:
(10 + 15i + (3ix + 2x))(2 + -3i) = 0
(10 + 15i + (3ix + 2x))(2 + -3i) = 0
(10 + 15i + 3ix + 2x)(2 + -3i) = 0

Multiply (10 + 15i + 3ix + 2x) * (2 + -3i)
(10(2 + -3i) + 15i * (2 + -3i) + 3ix * (2 + -3i) + 2x * (2 + -3i)) = 0
((2 * 10 + -3i * 10) + 15i * (2 + -3i) + 3ix * (2 + -3i) + 2x * (2 + -3i)) = 0
((20 + -30i) + 15i * (2 + -3i) + 3ix * (2 + -3i) + 2x * (2 + -3i)) = 0
(20 + -30i + (2 * 15i + -3i * 15i) + 3ix * (2 + -3i) + 2x * (2 + -3i)) = 0
(20 + -30i + (30i + -45i2) + 3ix * (2 + -3i) + 2x * (2 + -3i)) = 0
(20 + -30i + 30i + -45i2 + (2 * 3ix + -3i * 3ix) + 2x * (2 + -3i)) = 0
(20 + -30i + 30i + -45i2 + (6ix + -9i2x) + 2x * (2 + -3i)) = 0
(20 + -30i + 30i + -45i2 + 6ix + -9i2x + (2 * 2x + -3i * 2x)) = 0

Reorder the terms:
(20 + -30i + 30i + -45i2 + 6ix + -9i2x + (-6ix + 4x)) = 0
(20 + -30i + 30i + -45i2 + 6ix + -9i2x + (-6ix + 4x)) = 0

Reorder the terms:
(20 + -30i + 30i + 6ix + -6ix + -45i2 + -9i2x + 4x) = 0

Combine like terms: -30i + 30i = 0
(20 + 0 + 6ix + -6ix + -45i2 + -9i2x + 4x) = 0
(20 + 6ix + -6ix + -45i2 + -9i2x + 4x) = 0

Combine like terms: 6ix + -6ix = 0
(20 + 0 + -45i2 + -9i2x + 4x) = 0
(20 + -45i2 + -9i2x + 4x) = 0

Solving
20 + -45i2 + -9i2x + 4x = 0

Solving for variable 'i'.

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

Add '-20' to each side of the equation.
20 + -45i2 + -9i2x + -20 + 4x = 0 + -20

Reorder the terms:
20 + -20 + -45i2 + -9i2x + 4x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -45i2 + -9i2x + 4x = 0 + -20
-45i2 + -9i2x + 4x = 0 + -20

Combine like terms: 0 + -20 = -20
-45i2 + -9i2x + 4x = -20

Add '-4x' to each side of the equation.
-45i2 + -9i2x + 4x + -4x = -20 + -4x

Combine like terms: 4x + -4x = 0
-45i2 + -9i2x + 0 = -20 + -4x
-45i2 + -9i2x = -20 + -4x

Reorder the terms:
20 + -45i2 + -9i2x + 4x = -20 + -4x + 20 + 4x

Reorder the terms:
20 + -45i2 + -9i2x + 4x = -20 + 20 + -4x + 4x

Combine like terms: -20 + 20 = 0
20 + -45i2 + -9i2x + 4x = 0 + -4x + 4x
20 + -45i2 + -9i2x + 4x = -4x + 4x

Combine like terms: -4x + 4x = 0
20 + -45i2 + -9i2x + 4x = 0

The solution to this equation could not be determined.

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