(6+7i)(-5-9i)=

Solution for (6+7i)(-5-9i)= equation:

Simplifying
(6 + 7i)(-5 + -9i) = 0

Multiply (6 + 7i) * (-5 + -9i)
(6(-5 + -9i) + 7i * (-5 + -9i)) = 0
((-5 * 6 + -9i * 6) + 7i * (-5 + -9i)) = 0
((-30 + -54i) + 7i * (-5 + -9i)) = 0
(-30 + -54i + (-5 * 7i + -9i * 7i)) = 0
(-30 + -54i + (-35i + -63i2)) = 0

Combine like terms: -54i + -35i = -89i
(-30 + -89i + -63i2) = 0

Solving
-30 + -89i + -63i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 89i + 63i2) = 0

Factor a trinomial.
-1((6 + 7i)(5 + 9i)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 7i)' equal to zero and attempt to solve:

Simplifying
6 + 7i = 0

Solving
6 + 7i = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7i = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7i = 0 + -6
7i = 0 + -6

Combine like terms: 0 + -6 = -6
7i = -6

Divide each side by '7'.
i = -0.8571428571

Simplifying
i = -0.8571428571
Subproblem 2
Set the factor '(5 + 9i)' equal to zero and attempt to solve:

Simplifying
5 + 9i = 0

Solving
5 + 9i = 0

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

Add '-5' to each side of the equation.
5 + -5 + 9i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9i = 0 + -5
9i = 0 + -5

Combine like terms: 0 + -5 = -5
9i = -5

Divide each side by '9'.
i = -0.5555555556

Simplifying
i = -0.5555555556
Solution
i = {-0.8571428571, -0.5555555556}