(6+2i)(9+i)=

Solution for (6+2i)(9+i)= equation:

Simplifying
(6 + 2i)(9 + i) = 0

Multiply (6 + 2i) * (9 + i)
(6(9 + i) + 2i * (9 + i)) = 0
((9 * 6 + i * 6) + 2i * (9 + i)) = 0
((54 + 6i) + 2i * (9 + i)) = 0
(54 + 6i + (9 * 2i + i * 2i)) = 0
(54 + 6i + (18i + 2i2)) = 0

Combine like terms: 6i + 18i = 24i
(54 + 24i + 2i2) = 0

Solving
54 + 24i + 2i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 12i + i2) = 0

Factor a trinomial.
2((9 + i)(3 + i)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(9 + i)' equal to zero and attempt to solve:

Simplifying
9 + i = 0

Solving
9 + i = 0

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

Add '-9' to each side of the equation.
9 + -9 + i = 0 + -9

Combine like terms: 9 + -9 = 0
0 + i = 0 + -9
i = 0 + -9

Combine like terms: 0 + -9 = -9
i = -9

Simplifying
i = -9
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 = {-9, -3}