(-3+2i)(-6-8i)=0

Solution for (-3+2i)(-6-8i)=0 equation:

Simplifying
(-3 + 2i)(-6 + -8i) = 0

Multiply (-3 + 2i) * (-6 + -8i)
(-3(-6 + -8i) + 2i * (-6 + -8i)) = 0
((-6 * -3 + -8i * -3) + 2i * (-6 + -8i)) = 0
((18 + 24i) + 2i * (-6 + -8i)) = 0
(18 + 24i + (-6 * 2i + -8i * 2i)) = 0
(18 + 24i + (-12i + -16i2)) = 0

Combine like terms: 24i + -12i = 12i
(18 + 12i + -16i2) = 0

Solving
18 + 12i + -16i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 6i + -8i2) = 0

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

Ignore the factor 2.
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 '(3 + 4i)' equal to zero and attempt to solve:

Simplifying
3 + 4i = 0

Solving
3 + 4i = 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 + 4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4i = 0 + -3
4i = 0 + -3

Combine like terms: 0 + -3 = -3
4i = -3

Divide each side by '4'.
i = -0.75

Simplifying
i = -0.75
Solution
i = {1.5, -0.75}