(3+2i)(1-5i)=

Solution for (3+2i)(1-5i)= equation:

Simplifying
(3 + 2i)(1 + -5i) = 0

Multiply (3 + 2i) * (1 + -5i)
(3(1 + -5i) + 2i * (1 + -5i)) = 0
((1 * 3 + -5i * 3) + 2i * (1 + -5i)) = 0
((3 + -15i) + 2i * (1 + -5i)) = 0
(3 + -15i + (1 * 2i + -5i * 2i)) = 0
(3 + -15i + (2i + -10i2)) = 0

Combine like terms: -15i + 2i = -13i
(3 + -13i + -10i2) = 0

Solving
3 + -13i + -10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(1 + -5i)(3 + 2i) = 0

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

Simplifying
1 + -5i = 0

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

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

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

Divide each side by '-5'.
i = 0.2

Simplifying
i = 0.2
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 = {0.2, -1.5}