(3+2i)(-9-8i)=

Solution for (3+2i)(-9-8i)= equation:

Simplifying
(3 + 2i)(-9 + -8i) = 0

Multiply (3 + 2i) * (-9 + -8i)
(3(-9 + -8i) + 2i * (-9 + -8i)) = 0
((-9 * 3 + -8i * 3) + 2i * (-9 + -8i)) = 0
((-27 + -24i) + 2i * (-9 + -8i)) = 0
(-27 + -24i + (-9 * 2i + -8i * 2i)) = 0
(-27 + -24i + (-18i + -16i2)) = 0

Combine like terms: -24i + -18i = -42i
(-27 + -42i + -16i2) = 0

Solving
-27 + -42i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(27 + 42i + 16i2) = 0

Factor a trinomial.
-1((3 + 2i)(9 + 8i)) = 0

Ignore the factor -1.
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 '(9 + 8i)' equal to zero and attempt to solve:

Simplifying
9 + 8i = 0

Solving
9 + 8i = 0

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

Add '-9' to each side of the equation.
9 + -9 + 8i = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 8i = 0 + -9
8i = 0 + -9

Combine like terms: 0 + -9 = -9
8i = -9

Divide each side by '8'.
i = -1.125

Simplifying
i = -1.125
Solution
i = {-1.5, -1.125}