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

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

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

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

Combine like terms: 2i + -9i = -7i
(6 + -7i + -3i2) = 0

Solving
6 + -7i + -3i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + -3i)(3 + i) = 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 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

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

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

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

Simplifying
i = -3
Solution
i = {0.6666666667, -3}