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

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

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

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

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

Solving
30 + 8i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 4i + -4i2) = 0

Factor a trinomial.
2((5 + -2i)(3 + 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 '(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 = {2.5, -1.5}