(-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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