(3+i)(6-8i)=

Solution for (3+i)(6-8i)= equation:

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

Multiply (3 + i) * (6 + -8i)
(3(6 + -8i) + i(6 + -8i)) = 0
((6 * 3 + -8i * 3) + i(6 + -8i)) = 0
((18 + -24i) + i(6 + -8i)) = 0
(18 + -24i + (6 * i + -8i * i)) = 0
(18 + -24i + (6i + -8i2)) = 0

Combine like terms: -24i + 6i = -18i
(18 + -18i + -8i2) = 0

Solving
18 + -18i + -8i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -9i + -4i2) = 0

Factor a trinomial.
2((3 + -4i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -4i)' equal to zero and attempt to solve:

Simplifying
3 + -4i = 0

Solving
3 + -4i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4i = 0 + -3
-4i = 0 + -3

Combine like terms: 0 + -3 = -3
-4i = -3

Divide each side by '-4'.
i = 0.75

Simplifying
i = 0.75
Subproblem 2
Set the factor '(3 + i)' equal to zero and attempt to solve:

Simplifying
3 + i = 0

Solving
3 + i = 0

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

Add '-3' to each side of the equation.
3 + -3 + i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + i = 0 + -3
i = 0 + -3

Combine like terms: 0 + -3 = -3
i = -3

Simplifying
i = -3
Solution
i = {0.75, -3}