(4-2i)(-3+i)=

Solution for (4-2i)(-3+i)= equation:

Simplifying
(4 + -2i)(-3 + i) = 0

Multiply (4 + -2i) * (-3 + i)
(4(-3 + i) + -2i * (-3 + i)) = 0
((-3 * 4 + i * 4) + -2i * (-3 + i)) = 0
((-12 + 4i) + -2i * (-3 + i)) = 0
(-12 + 4i + (-3 * -2i + i * -2i)) = 0
(-12 + 4i + (6i + -2i2)) = 0

Combine like terms: 4i + 6i = 10i
(-12 + 10i + -2i2) = 0

Solving
-12 + 10i + -2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 5i + -1i2) = 0

Factor a trinomial.
2((-3 + i)(2 + -1i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + i)' equal to zero and attempt to solve:

Simplifying
-3 + i = 0

Solving
-3 + i = 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 + i = 0 + 3

Combine like terms: -3 + 3 = 0
0 + i = 0 + 3
i = 0 + 3

Combine like terms: 0 + 3 = 3
i = 3

Simplifying
i = 3
Subproblem 2
Set the factor '(2 + -1i)' equal to zero and attempt to solve:

Simplifying
2 + -1i = 0

Solving
2 + -1i = 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 + -1i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1i = 0 + -2
-1i = 0 + -2

Combine like terms: 0 + -2 = -2
-1i = -2

Divide each side by '-1'.
i = 2

Simplifying
i = 2
Solution
i = {3, 2}