(2-5i)(6+4i)=

Solution for (2-5i)(6+4i)= equation:

Simplifying
(2 + -5i)(6 + 4i) = 0

Multiply (2 + -5i) * (6 + 4i)
(2(6 + 4i) + -5i * (6 + 4i)) = 0
((6 * 2 + 4i * 2) + -5i * (6 + 4i)) = 0
((12 + 8i) + -5i * (6 + 4i)) = 0
(12 + 8i + (6 * -5i + 4i * -5i)) = 0
(12 + 8i + (-30i + -20i2)) = 0

Combine like terms: 8i + -30i = -22i
(12 + -22i + -20i2) = 0

Solving
12 + -22i + -20i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -11i + -10i2) = 0

Factor a trinomial.
2((2 + -5i)(3 + 2i)) = 0

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

Simplifying
2 + -5i = 0

Solving
2 + -5i = 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 + -5i = 0 + -2

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

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

Divide each side by '-5'.
i = 0.4

Simplifying
i = 0.4
Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve:

Simplifying
3 + 2i = 0

Solving
3 + 2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Solution
i = {0.4, -1.5}