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

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

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

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

Combine like terms: 4i + -30i = -26i
(24 + -26i + -5i2) = 0

Solving
24 + -26i + -5i2 = 0

Solving for variable 'i'.

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

Subproblem 1
Set the factor '(4 + -5i)' equal to zero and attempt to solve:

Simplifying
4 + -5i = 0

Solving
4 + -5i = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5i = 0 + -4

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

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

Divide each side by '-5'.
i = 0.8

Simplifying
i = 0.8
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 = {0.8, -6}