(6-5i)(3+2i)=0

Solution for (6-5i)(3+2i)=0 equation:

Simplifying
(6 + -5i)(3 + 2i) = 0

Multiply (6 + -5i) * (3 + 2i)
(6(3 + 2i) + -5i * (3 + 2i)) = 0
((3 * 6 + 2i * 6) + -5i * (3 + 2i)) = 0
((18 + 12i) + -5i * (3 + 2i)) = 0
(18 + 12i + (3 * -5i + 2i * -5i)) = 0
(18 + 12i + (-15i + -10i2)) = 0

Combine like terms: 12i + -15i = -3i
(18 + -3i + -10i2) = 0

Solving
18 + -3i + -10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -5i)(3 + 2i) = 0

Subproblem 1
Set the factor '(6 + -5i)' equal to zero and attempt to solve:

Simplifying
6 + -5i = 0

Solving
6 + -5i = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5i = 0 + -6
-5i = 0 + -6

Combine like terms: 0 + -6 = -6
-5i = -6

Divide each side by '-5'.
i = 1.2

Simplifying
i = 1.2
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 = {1.2, -1.5}