(-3+2i)(1-4i)=

Solution for (-3+2i)(1-4i)= equation:

Simplifying
(-3 + 2i)(1 + -4i) = 0

Multiply (-3 + 2i) * (1 + -4i)
(-3(1 + -4i) + 2i * (1 + -4i)) = 0
((1 * -3 + -4i * -3) + 2i * (1 + -4i)) = 0
((-3 + 12i) + 2i * (1 + -4i)) = 0
(-3 + 12i + (1 * 2i + -4i * 2i)) = 0
(-3 + 12i + (2i + -8i2)) = 0

Combine like terms: 12i + 2i = 14i
(-3 + 14i + -8i2) = 0

Solving
-3 + 14i + -8i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(-3 + 2i)(1 + -4i) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + -4i)' equal to zero and attempt to solve:

Simplifying
1 + -4i = 0

Solving
1 + -4i = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4i = 0 + -1
-4i = 0 + -1

Combine like terms: 0 + -1 = -1
-4i = -1

Divide each side by '-4'.
i = 0.25

Simplifying
i = 0.25
Solution
i = {1.5, 0.25}