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

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

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

Reorder the terms:
(-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 = 59i
(-30 + 59i + -28i2) = 0

Solving
-30 + 59i + -28i2 = 0

Solving for variable 'i'.

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

Subproblem 1
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
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 = {1.25, 0.8571428571}