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

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

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

Multiply (3 + 2i) * (2 + 5i)
(3(2 + 5i) + 2i * (2 + 5i)) = 0
((2 * 3 + 5i * 3) + 2i * (2 + 5i)) = 0
((6 + 15i) + 2i * (2 + 5i)) = 0
(6 + 15i + (2 * 2i + 5i * 2i)) = 0
(6 + 15i + (4i + 10i2)) = 0

Combine like terms: 15i + 4i = 19i
(6 + 19i + 10i2) = 0

Solving
6 + 19i + 10i2 = 0

Solving for variable 'i'.

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

Simplifying
2 + 5i = 0

Solving
2 + 5i = 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 + 5i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5i = 0 + -2
5i = 0 + -2

Combine like terms: 0 + -2 = -2
5i = -2

Divide each side by '5'.
i = -0.4

Simplifying
i = -0.4
Solution
i = {-1.5, -0.4}