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

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 '(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
Solution
i = {1.5, -1.2}