(5+4i)(6-7i)=0

Solution for (5+4i)(6-7i)=0 equation:

Simplifying
(5 + 4i)(6 + -7i) = 0

Multiply (5 + 4i) * (6 + -7i)
(5(6 + -7i) + 4i * (6 + -7i)) = 0
((6 * 5 + -7i * 5) + 4i * (6 + -7i)) = 0
((30 + -35i) + 4i * (6 + -7i)) = 0
(30 + -35i + (6 * 4i + -7i * 4i)) = 0
(30 + -35i + (24i + -28i2)) = 0

Combine like terms: -35i + 24i = -11i
(30 + -11i + -28i2) = 0

Solving
30 + -11i + -28i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(6 + -7i)(5 + 4i) = 0

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 + 4i)' equal to zero and attempt to solve:

Simplifying
5 + 4i = 0

Solving
5 + 4i = 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 + 4i = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4i = 0 + -5
4i = 0 + -5

Combine like terms: 0 + -5 = -5
4i = -5

Divide each side by '4'.
i = -1.25

Simplifying
i = -1.25
Solution
i = {0.8571428571, -1.25}