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

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

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

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

Combine like terms: 4i + -9i = -5i
(6 + -5i + -6i2) = 0

Solving
6 + -5i + -6i2 = 0

Solving for variable 'i'.

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

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

Simplifying
2 + -3i = 0

Solving
2 + -3i = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3i = 0 + -2
-3i = 0 + -2

Combine like terms: 0 + -2 = -2
-3i = -2

Divide each side by '-3'.
i = 0.6666666667

Simplifying
i = 0.6666666667
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 = {0.6666666667, -1.5}