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

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

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

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

Combine like terms: 9i + 2i = 11i
(6 + 11i + 3i2) = 0

Solving
6 + 11i + 3i2 = 0

Solving for variable 'i'.

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

Subproblem 1
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
Subproblem 2
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
Solution
i = {-3, -0.6666666667}