(3+4i)(5-2i)=

Solution for (3+4i)(5-2i)= equation:

Simplifying
(3 + 4i)(5 + -2i) = 0

Multiply (3 + 4i) * (5 + -2i)
(3(5 + -2i) + 4i * (5 + -2i)) = 0
((5 * 3 + -2i * 3) + 4i * (5 + -2i)) = 0
((15 + -6i) + 4i * (5 + -2i)) = 0
(15 + -6i + (5 * 4i + -2i * 4i)) = 0
(15 + -6i + (20i + -8i2)) = 0

Combine like terms: -6i + 20i = 14i
(15 + 14i + -8i2) = 0

Solving
15 + 14i + -8i2 = 0

Solving for variable 'i'.

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

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 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {2.5, -0.75}