(6+i)(8-i)=

Solution for (6+i)(8-i)= equation:

Simplifying
(6 + i)(8 + -1i) = 0

Multiply (6 + i) * (8 + -1i)
(6(8 + -1i) + i(8 + -1i)) = 0
((8 * 6 + -1i * 6) + i(8 + -1i)) = 0
((48 + -6i) + i(8 + -1i)) = 0
(48 + -6i + (8 * i + -1i * i)) = 0
(48 + -6i + (8i + -1i2)) = 0

Combine like terms: -6i + 8i = 2i
(48 + 2i + -1i2) = 0

Solving
48 + 2i + -1i2 = 0

Solving for variable 'i'.

Factor a trinomial.
(8 + -1i)(6 + i) = 0

Subproblem 1
Set the factor '(8 + -1i)' equal to zero and attempt to solve:

Simplifying
8 + -1i = 0

Solving
8 + -1i = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1i = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1i = 0 + -8
-1i = 0 + -8

Combine like terms: 0 + -8 = -8
-1i = -8

Divide each side by '-1'.
i = 8

Simplifying
i = 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 = {8, -6}