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

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

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

Multiply (3 + -3i) * (4 + 2i)
(3(4 + 2i) + -3i * (4 + 2i)) = 0
((4 * 3 + 2i * 3) + -3i * (4 + 2i)) = 0
((12 + 6i) + -3i * (4 + 2i)) = 0
(12 + 6i + (4 * -3i + 2i * -3i)) = 0
(12 + 6i + (-12i + -6i2)) = 0

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

Solving
12 + -6i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(2 + -1i + -1i2) = 0

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

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

Simplifying
1 + -1i = 0

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

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

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

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

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

Simplifying
2 + i = 0

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

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

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

Simplifying
i = -2
Solution
i = {1, -2}