(8+i)(6+2i)=0

Solution for (8+i)(6+2i)=0 equation:

Simplifying
(8 + i)(6 + 2i) = 0

Multiply (8 + i) * (6 + 2i)
(8(6 + 2i) + i(6 + 2i)) = 0
((6 * 8 + 2i * 8) + i(6 + 2i)) = 0
((48 + 16i) + i(6 + 2i)) = 0
(48 + 16i + (6 * i + 2i * i)) = 0
(48 + 16i + (6i + 2i2)) = 0

Combine like terms: 16i + 6i = 22i
(48 + 22i + 2i2) = 0

Solving
48 + 22i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 11i + i2) = 0

Factor a trinomial.
2((8 + i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + i)' equal to zero and attempt to solve:

Simplifying
8 + i = 0

Solving
8 + i = 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 + i = 0 + -8

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

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

Simplifying
i = -8
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 = {-8, -3}