(-5+-2i)x(-2+4i)=

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Solution for (-5+-2i)x(-2+4i)= equation: 


Simplifying
(-5 + -2i) * x(-2 + 4i) = 0

Reorder the terms for easier multiplication:
x(-5 + -2i)(-2 + 4i) = 0

Multiply (-5 + -2i) * (-2 + 4i)
x(-5(-2 + 4i) + -2i * (-2 + 4i)) = 0
x((-2 * -5 + 4i * -5) + -2i * (-2 + 4i)) = 0
x((10 + -20i) + -2i * (-2 + 4i)) = 0
x(10 + -20i + (-2 * -2i + 4i * -2i)) = 0
x(10 + -20i + (4i + -8i2)) = 0

Combine like terms: -20i + 4i = -16i
x(10 + -16i + -8i2) = 0
(10 * x + -16i * x + -8i2 * x) = 0

Reorder the terms:
(-16ix + -8i2x + 10x) = 0
(-16ix + -8i2x + 10x) = 0

Solving
-16ix + -8i2x + 10x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-8i + -4i2 + 5) = 0

Factor a trinomial.
2x((-2i + -5)(2i + -1)) = 0

Ignore the factor 2.

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

Simplifying
x = 0

Solving
x = 0

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

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

Simplifying
0 = -1x

The solution to this equation could not be determined.

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

Subproblem 2
Set the factor '(-2i + -5)' equal to zero and attempt to solve:

Simplifying
-2i + -5 = 0

Reorder the terms:
-5 + -2i = 0

Solving
-5 + -2i = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2i = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2i = 0 + 5
-2i = 0 + 5

Combine like terms: 0 + 5 = 5
-2i = 5

Divide each side by '-2'.
i = -2.5

Simplifying
i = -2.5

Subproblem 3
Set the factor '(2i + -1)' equal to zero and attempt to solve:

Simplifying
2i + -1 = 0

Reorder the terms:
-1 + 2i = 0

Solving
-1 + 2i = 0

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

Add '1' to each side of the equation.
-1 + 1 + 2i = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2i = 0 + 1
2i = 0 + 1

Combine like terms: 0 + 1 = 1
2i = 1

Divide each side by '2'.
i = 0.5

Simplifying
i = 0.5
Solution
i = {-2.5, 0.5}

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