(2-8i)(5-i)=

Solution for (2-8i)(5-i)= equation:

Simplifying
(2 + -8i)(5 + -1i) = 0

Multiply (2 + -8i) * (5 + -1i)
(2(5 + -1i) + -8i * (5 + -1i)) = 0
((5 * 2 + -1i * 2) + -8i * (5 + -1i)) = 0
((10 + -2i) + -8i * (5 + -1i)) = 0
(10 + -2i + (5 * -8i + -1i * -8i)) = 0
(10 + -2i + (-40i + 8i2)) = 0

Combine like terms: -2i + -40i = -42i
(10 + -42i + 8i2) = 0

Solving
10 + -42i + 8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -21i + 4i2) = 0

Factor a trinomial.
2((1 + -4i)(5 + -1i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -4i)' equal to zero and attempt to solve:

Simplifying
1 + -4i = 0

Solving
1 + -4i = 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 + -4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4i = 0 + -1
-4i = 0 + -1

Combine like terms: 0 + -1 = -1
-4i = -1

Divide each side by '-4'.
i = 0.25

Simplifying
i = 0.25
Subproblem 2
Set the factor '(5 + -1i)' equal to zero and attempt to solve:

Simplifying
5 + -1i = 0

Solving
5 + -1i = 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 + -1i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1i = 0 + -5
-1i = 0 + -5

Combine like terms: 0 + -5 = -5
-1i = -5

Divide each side by '-1'.
i = 5

Simplifying
i = 5
Solution
i = {0.25, 5}