(2+6i)(7-9i)=

Solution for (2+6i)(7-9i)= equation:

Simplifying
(2 + 6i)(7 + -9i) = 0

Multiply (2 + 6i) * (7 + -9i)
(2(7 + -9i) + 6i * (7 + -9i)) = 0
((7 * 2 + -9i * 2) + 6i * (7 + -9i)) = 0
((14 + -18i) + 6i * (7 + -9i)) = 0
(14 + -18i + (7 * 6i + -9i * 6i)) = 0
(14 + -18i + (42i + -54i2)) = 0

Combine like terms: -18i + 42i = 24i
(14 + 24i + -54i2) = 0

Solving
14 + 24i + -54i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 12i + -27i2) = 0

Factor a trinomial.
2((7 + -9i)(1 + 3i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -9i)' equal to zero and attempt to solve:

Simplifying
7 + -9i = 0

Solving
7 + -9i = 0

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

Add '-7' to each side of the equation.
7 + -7 + -9i = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -9i = 0 + -7
-9i = 0 + -7

Combine like terms: 0 + -7 = -7
-9i = -7

Divide each side by '-9'.
i = 0.7777777778

Simplifying
i = 0.7777777778
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 = {0.7777777778, -0.3333333333}