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

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

Simplifying
(-3 + 5i)(2 + -1i) = 0

Multiply (-3 + 5i) * (2 + -1i)
(-3(2 + -1i) + 5i * (2 + -1i)) = 0
((2 * -3 + -1i * -3) + 5i * (2 + -1i)) = 0
((-6 + 3i) + 5i * (2 + -1i)) = 0
(-6 + 3i + (2 * 5i + -1i * 5i)) = 0
(-6 + 3i + (10i + -5i2)) = 0

Combine like terms: 3i + 10i = 13i
(-6 + 13i + -5i2) = 0

Solving
-6 + 13i + -5i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-2 + i)(3 + -5i) = 0

Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve:

Simplifying
-2 + i = 0

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

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

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

Simplifying
i = 2
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 = {2, 0.6}