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

Solution for (3+2i)(4-2i)=0 equation:

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

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

Combine like terms: -6i + 8i = 2i
(12 + 2i + -4i2) = 0

Solving
12 + 2i + -4i2 = 0

Solving for variable 'i'.

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

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

Ignore the factor 2.
Subproblem 1
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
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 = {2, -1.5}