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

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

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

Multiply (-4 + i) * (3 + -2i)
(-4(3 + -2i) + i(3 + -2i)) = 0
((3 * -4 + -2i * -4) + i(3 + -2i)) = 0
((-12 + 8i) + i(3 + -2i)) = 0
(-12 + 8i + (3 * i + -2i * i)) = 0
(-12 + 8i + (3i + -2i2)) = 0

Combine like terms: 8i + 3i = 11i
(-12 + 11i + -2i2) = 0

Solving
-12 + 11i + -2i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-4 + i)(3 + -2i) = 0

Subproblem 1
Set the factor '(-4 + i)' equal to zero and attempt to solve:

Simplifying
-4 + i = 0

Solving
-4 + i = 0

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

Add '4' to each side of the equation.
-4 + 4 + i = 0 + 4

Combine like terms: -4 + 4 = 0
0 + i = 0 + 4
i = 0 + 4

Combine like terms: 0 + 4 = 4
i = 4

Simplifying
i = 4
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 = {4, 1.5}