(3+i)(2+2i)=

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

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

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

Combine like terms: 6i + 2i = 8i
(6 + 8i + 2i2) = 0

Solving
6 + 8i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 4i + i2) = 0

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

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

Simplifying
1 + i = 0

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

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

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

Simplifying
i = -1
Solution
i = {-3, -1}