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

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

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

Multiply (3 + 2i) * (3 + -4i)
(3(3 + -4i) + 2i * (3 + -4i)) = 0
((3 * 3 + -4i * 3) + 2i * (3 + -4i)) = 0
((9 + -12i) + 2i * (3 + -4i)) = 0
(9 + -12i + (3 * 2i + -4i * 2i)) = 0
(9 + -12i + (6i + -8i2)) = 0

Combine like terms: -12i + 6i = -6i
(9 + -6i + -8i2) = 0

Solving
9 + -6i + -8i2 = 0

Solving for variable 'i'.

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

Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 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 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75
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 = {0.75, -1.5}