(1+2i)(4+2i)=

Solution for (1+2i)(4+2i)= equation:

Simplifying
(1 + 2i)(4 + 2i) = 0

Multiply (1 + 2i) * (4 + 2i)
(1(4 + 2i) + 2i * (4 + 2i)) = 0
((4 * 1 + 2i * 1) + 2i * (4 + 2i)) = 0
((4 + 2i) + 2i * (4 + 2i)) = 0
(4 + 2i + (4 * 2i + 2i * 2i)) = 0
(4 + 2i + (8i + 4i2)) = 0

Combine like terms: 2i + 8i = 10i
(4 + 10i + 4i2) = 0

Solving
4 + 10i + 4i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
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
Solution
i = {-2, -0.5}