(4+i)(2+2i)=

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

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

Multiply (4 + i) * (2 + 2i)
(4(2 + 2i) + i(2 + 2i)) = 0
((2 * 4 + 2i * 4) + i(2 + 2i)) = 0
((8 + 8i) + i(2 + 2i)) = 0
(8 + 8i + (2 * i + 2i * i)) = 0
(8 + 8i + (2i + 2i2)) = 0

Combine like terms: 8i + 2i = 10i
(8 + 10i + 2i2) = 0

Solving
8 + 10i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 5i + i2) = 0

Factor a trinomial.
2((4 + i)(1 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + i)' equal to zero and attempt to solve:

Simplifying
4 + i = 0

Solving
4 + i = 0

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

Add '-4' to each side of the equation.
4 + -4 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
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 = {-4, -1}