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

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

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

Multiply (3 + 2i) * (4 + i)
(3(4 + i) + 2i * (4 + i)) = 0
((4 * 3 + i * 3) + 2i * (4 + i)) = 0
((12 + 3i) + 2i * (4 + i)) = 0
(12 + 3i + (4 * 2i + i * 2i)) = 0
(12 + 3i + (8i + 2i2)) = 0

Combine like terms: 3i + 8i = 11i
(12 + 11i + 2i2) = 0

Solving
12 + 11i + 2i2 = 0

Solving for variable 'i'.

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

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 '(3 + 2i)' equal to zero and attempt to solve:

Simplifying
3 + 2i = 0

Solving
3 + 2i = 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 + 2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2i = 0 + -3
2i = 0 + -3

Combine like terms: 0 + -3 = -3
2i = -3

Divide each side by '2'.
i = -1.5

Simplifying
i = -1.5
Solution
i = {-4, -1.5}