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

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

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

Multiply (6 + 2i) * (5 + -4i)
(6(5 + -4i) + 2i * (5 + -4i)) = 0
((5 * 6 + -4i * 6) + 2i * (5 + -4i)) = 0
((30 + -24i) + 2i * (5 + -4i)) = 0
(30 + -24i + (5 * 2i + -4i * 2i)) = 0
(30 + -24i + (10i + -8i2)) = 0

Combine like terms: -24i + 10i = -14i
(30 + -14i + -8i2) = 0

Solving
30 + -14i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + -7i + -4i2) = 0

Factor a trinomial.
2((5 + -4i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve:

Simplifying
5 + -4i = 0

Solving
5 + -4i = 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 + -4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4i = 0 + -5
-4i = 0 + -5

Combine like terms: 0 + -5 = -5
-4i = -5

Divide each side by '-4'.
i = 1.25

Simplifying
i = 1.25
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 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 + i = 0 + -3

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

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

Simplifying
i = -3
Solution
i = {1.25, -3}