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

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

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

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

Combine like terms: 5i + -24i = -19i
(30 + -19i + -4i2) = 0

Solving
30 + -19i + -4i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(5 + -4i)(6 + i) = 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 + i)' equal to zero and attempt to solve:

Simplifying
6 + i = 0

Solving
6 + i = 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 + i = 0 + -6

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

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

Simplifying
i = -6
Solution
i = {1.25, -6}