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

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

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

Multiply (3 + -9i) * (4 + 9i)
(3(4 + 9i) + -9i * (4 + 9i)) = 0
((4 * 3 + 9i * 3) + -9i * (4 + 9i)) = 0
((12 + 27i) + -9i * (4 + 9i)) = 0
(12 + 27i + (4 * -9i + 9i * -9i)) = 0
(12 + 27i + (-36i + -81i2)) = 0

Combine like terms: 27i + -36i = -9i
(12 + -9i + -81i2) = 0

Solving
12 + -9i + -81i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -3i + -27i2) = 0

Factor a trinomial.
3((1 + -3i)(4 + 9i)) = 0

Ignore the factor 3.
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 '(4 + 9i)' equal to zero and attempt to solve:

Simplifying
4 + 9i = 0

Solving
4 + 9i = 0

Move all terms containing i to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 9i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 9i = 0 + -4
9i = 0 + -4

Combine like terms: 0 + -4 = -4
9i = -4

Divide each side by '9'.
i = -0.4444444444

Simplifying
i = -0.4444444444
Solution
i = {0.3333333333, -0.4444444444}