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

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

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

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

Combine like terms: 35i + -54i = -19i
(30 + -19i + -63i2) = 0

Solving
30 + -19i + -63i2 = 0

Solving for variable 'i'.

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

Subproblem 1
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
Subproblem 2
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
Solution
i = {0.5555555556, -0.8571428571}