(-2+6i)(3-4i)=0

Solution for (-2+6i)(3-4i)=0 equation:

Simplifying
(-2 + 6i)(3 + -4i) = 0

Multiply (-2 + 6i) * (3 + -4i)
(-2(3 + -4i) + 6i * (3 + -4i)) = 0
((3 * -2 + -4i * -2) + 6i * (3 + -4i)) = 0
((-6 + 8i) + 6i * (3 + -4i)) = 0
(-6 + 8i + (3 * 6i + -4i * 6i)) = 0
(-6 + 8i + (18i + -24i2)) = 0

Combine like terms: 8i + 18i = 26i
(-6 + 26i + -24i2) = 0

Solving
-6 + 26i + -24i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 13i + -12i2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -3i)' equal to zero and attempt to solve:

Simplifying
1 + -3i = 0

Solving
1 + -3i = 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 + -3i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3i = 0 + -1
-3i = 0 + -1

Combine like terms: 0 + -1 = -1
-3i = -1

Divide each side by '-3'.
i = 0.3333333333

Simplifying
i = 0.3333333333
Solution
i = {0.75, 0.3333333333}