(3+i)(6-2i)=

Solution for (3+i)(6-2i)= equation:

Simplifying
(3 + i)(6 + -2i) = 0

Multiply (3 + i) * (6 + -2i)
(3(6 + -2i) + i(6 + -2i)) = 0
((6 * 3 + -2i * 3) + i(6 + -2i)) = 0
((18 + -6i) + i(6 + -2i)) = 0
(18 + -6i + (6 * i + -2i * i)) = 0
(18 + -6i + (6i + -2i2)) = 0

Combine like terms: -6i + 6i = 0
(18 + 0 + -2i2) = 0
(18 + -2i2) = 0

Solving
18 + -2i2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-18' to each side of the equation.
18 + -18 + -2i2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -2i2 = 0 + -18
-2i2 = 0 + -18

Combine like terms: 0 + -18 = -18
-2i2 = -18

Divide each side by '-2'.
i2 = 9

Simplifying
i2 = 9

Take the square root of each side:
i = {-3, 3}