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

Solution for (2+3i)(-3+5i)= 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 = 1i
(-6 + 1i + 15i2) = 0

Solving
-6 + 1i + 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}