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

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


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

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

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

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

Reorder the terms:
(-10 + 15i + 5x + (3ix + -2x + x2)) = 0
(-10 + 15i + 5x + (3ix + -2x + x2)) = 0

Reorder the terms:
(-10 + 15i + 3ix + 5x + -2x + x2) = 0

Combine like terms: 5x + -2x = 3x
(-10 + 15i + 3ix + 3x + x2) = 0

Solving
-10 + 15i + 3ix + 3x + x2 = 0

Solving for variable 'i'.

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

Add '10' to each side of the equation.
-10 + 15i + 3ix + 3x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 15i + 3ix + 3x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 15i + 3ix + 3x + x2 = 0 + 10
15i + 3ix + 3x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
15i + 3ix + 3x + x2 = 10

Add '-3x' to each side of the equation.
15i + 3ix + 3x + -3x + x2 = 10 + -3x

Combine like terms: 3x + -3x = 0
15i + 3ix + 0 + x2 = 10 + -3x
15i + 3ix + x2 = 10 + -3x

Add '-1x2' to each side of the equation.
15i + 3ix + x2 + -1x2 = 10 + -3x + -1x2

Combine like terms: x2 + -1x2 = 0
15i + 3ix + 0 = 10 + -3x + -1x2
15i + 3ix = 10 + -3x + -1x2

Reorder the terms:
-10 + 15i + 3ix + 3x + x2 = 10 + -3x + -1x2 + -10 + 3x + x2

Reorder the terms:
-10 + 15i + 3ix + 3x + x2 = 10 + -10 + -3x + 3x + -1x2 + x2

Combine like terms: 10 + -10 = 0
-10 + 15i + 3ix + 3x + x2 = 0 + -3x + 3x + -1x2 + x2
-10 + 15i + 3ix + 3x + x2 = -3x + 3x + -1x2 + x2

Combine like terms: -3x + 3x = 0
-10 + 15i + 3ix + 3x + x2 = 0 + -1x2 + x2
-10 + 15i + 3ix + 3x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-10 + 15i + 3ix + 3x + x2 = 0

The solution to this equation could not be determined.

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