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

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

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

Multiply (-3 + 2i) * (5 + -1i)
(-3(5 + -1i) + 2i * (5 + -1i)) = 0
((5 * -3 + -1i * -3) + 2i * (5 + -1i)) = 0
((-15 + 3i) + 2i * (5 + -1i)) = 0
(-15 + 3i + (5 * 2i + -1i * 2i)) = 0
(-15 + 3i + (10i + -2i2)) = 0

Combine like terms: 3i + 10i = 13i
(-15 + 13i + -2i2) = 0

Solving
-15 + 13i + -2i2 = 0

Solving for variable 'i'.

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

Subproblem 1
Set the factor '(-5 + i)' equal to zero and attempt to solve:

Simplifying
-5 + i = 0

Solving
-5 + i = 0

Move all terms containing i to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + i = 0 + 5

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

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

Simplifying
i = 5
Subproblem 2
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
Solution
i = {5, 1.5}