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

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

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

Multiply (6 + 2i) * (3 + -6i)
(6(3 + -6i) + 2i * (3 + -6i)) = 0
((3 * 6 + -6i * 6) + 2i * (3 + -6i)) = 0
((18 + -36i) + 2i * (3 + -6i)) = 0
(18 + -36i + (3 * 2i + -6i * 2i)) = 0
(18 + -36i + (6i + -12i2)) = 0

Combine like terms: -36i + 6i = -30i
(18 + -30i + -12i2) = 0

Solving
18 + -30i + -12i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -5i + -2i2) = 0

Factor a trinomial.
6((1 + -2i)(3 + i)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

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

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

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

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
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 = {0.5, -3}