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

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

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

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

Combine like terms: 6i + 15i = 21i
(9 + 21i + 10i2) = 0

Solving
9 + 21i + 10i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(3 + 2i)(3 + 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 '(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 = {-1.5, -0.6}