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

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

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

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

Combine like terms: -4i + 15i = 11i
(6 + 11i + -10i2) = 0

Solving
6 + 11i + -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}