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

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

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

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

Combine like terms: 20i + 4i = 24i
(-10 + 24i + -8i2) = 0

Solving
-10 + 24i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 12i + -4i2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + 2i)' equal to zero and attempt to solve:

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

Simplifying
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}