(-2+4i)(3+9i)=

Solution for (-2+4i)(3+9i)= equation:

Simplifying
(-2 + 4i)(3 + 9i) = 0

Multiply (-2 + 4i) * (3 + 9i)
(-2(3 + 9i) + 4i * (3 + 9i)) = 0
((3 * -2 + 9i * -2) + 4i * (3 + 9i)) = 0
((-6 + -18i) + 4i * (3 + 9i)) = 0
(-6 + -18i + (3 * 4i + 9i * 4i)) = 0
(-6 + -18i + (12i + 36i2)) = 0

Combine like terms: -18i + 12i = -6i
(-6 + -6i + 36i2) = 0

Solving
-6 + -6i + 36i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -1i + 6i2) = 0

Factor a trinomial.
6((-1 + -3i)(1 + -2i)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -2i)' equal to zero and attempt to solve:

Simplifying
1 + -2i = 0

Solving
1 + -2i = 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 + -2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2i = 0 + -1
-2i = 0 + -1

Combine like terms: 0 + -1 = -1
-2i = -1

Divide each side by '-2'.
i = 0.5

Simplifying
i = 0.5
Solution
i = {-0.3333333333, 0.5}