(5-10i)(4+2i)=

Solution for (5-10i)(4+2i)= equation:

Simplifying
(5 + -10i)(4 + 2i) = 0

Multiply (5 + -10i) * (4 + 2i)
(5(4 + 2i) + -10i * (4 + 2i)) = 0
((4 * 5 + 2i * 5) + -10i * (4 + 2i)) = 0
((20 + 10i) + -10i * (4 + 2i)) = 0
(20 + 10i + (4 * -10i + 2i * -10i)) = 0
(20 + 10i + (-40i + -20i2)) = 0

Combine like terms: 10i + -40i = -30i
(20 + -30i + -20i2) = 0

Solving
20 + -30i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '10'.
10(2 + -3i + -2i2) = 0

Factor a trinomial.
10((1 + -2i)(2 + i)) = 0

Ignore the factor 10.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + i)' equal to zero and attempt to solve:

Simplifying
2 + i = 0

Solving
2 + i = 0

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

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

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

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

Simplifying
i = -2
Solution
i = {0.5, -2}