(3-2i)(9-3i)=

Solution for (3-2i)(9-3i)= equation:

Simplifying
(3 + -2i)(9 + -3i) = 0

Multiply (3 + -2i) * (9 + -3i)
(3(9 + -3i) + -2i * (9 + -3i)) = 0
((9 * 3 + -3i * 3) + -2i * (9 + -3i)) = 0
((27 + -9i) + -2i * (9 + -3i)) = 0
(27 + -9i + (9 * -2i + -3i * -2i)) = 0
(27 + -9i + (-18i + 6i2)) = 0

Combine like terms: -9i + -18i = -27i
(27 + -27i + 6i2) = 0

Solving
27 + -27i + 6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -9i + 2i2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 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 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Divide each side by '-1'.
i = 3

Simplifying
i = 3
Solution
i = {1.5, 3}