(3+i)(2-i)=

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

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

Multiply (3 + i) * (2 + -1i)
(3(2 + -1i) + i(2 + -1i)) = 0
((2 * 3 + -1i * 3) + i(2 + -1i)) = 0
((6 + -3i) + i(2 + -1i)) = 0
(6 + -3i + (2 * i + -1i * i)) = 0
(6 + -3i + (2i + -1i2)) = 0

Combine like terms: -3i + 2i = -1i
(6 + -1i + -1i2) = 0

Solving
6 + -1i + -1i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
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 = {2, -3}