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

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

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

Multiply (2 + 3i) * (3 + 5i)
(2(3 + 5i) + 3i * (3 + 5i)) = 0
((3 * 2 + 5i * 2) + 3i * (3 + 5i)) = 0
((6 + 10i) + 3i * (3 + 5i)) = 0
(6 + 10i + (3 * 3i + 5i * 3i)) = 0
(6 + 10i + (9i + 15i2)) = 0

Combine like terms: 10i + 9i = 19i
(6 + 19i + 15i2) = 0

Solving
6 + 19i + 15i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(2 + 3i)(3 + 5i) = 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 + 5i)' equal to zero and attempt to solve:

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5i = 0 + -3
5i = 0 + -3

Combine like terms: 0 + -3 = -3
5i = -3

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {-0.6666666667, -0.6}