(3-2i)(5+1)(4-2i)=

Solution for (3-2i)(5+1)(4-2i)= equation:

Simplifying
(3 + -2i)(5 + 1)(4 + -2i) = 0

Combine like terms: 5 + 1 = 6
(3 + -2i)(6)(4 + -2i) = 0

Reorder the terms for easier multiplication:
6(3 + -2i)(4 + -2i) = 0

Multiply (3 + -2i) * (4 + -2i)
6(3(4 + -2i) + -2i * (4 + -2i)) = 0
6((4 * 3 + -2i * 3) + -2i * (4 + -2i)) = 0
6((12 + -6i) + -2i * (4 + -2i)) = 0
6(12 + -6i + (4 * -2i + -2i * -2i)) = 0
6(12 + -6i + (-8i + 4i2)) = 0

Combine like terms: -6i + -8i = -14i
6(12 + -14i + 4i2) = 0
(12 * 6 + -14i * 6 + 4i2 * 6) = 0
(72 + -84i + 24i2) = 0

Solving
72 + -84i + 24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '12'.
12(6 + -7i + 2i2) = 0

Factor a trinomial.
12((3 + -2i)(2 + -1i)) = 0

Ignore the factor 12.
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 '(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 = {1.5, 2}