(6+3i)(3+i)=0

Solution for (6+3i)(3+i)=0 equation:

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

Multiply (6 + 3i) * (3 + i)
(6(3 + i) + 3i * (3 + i)) = 0
((3 * 6 + i * 6) + 3i * (3 + i)) = 0
((18 + 6i) + 3i * (3 + i)) = 0
(18 + 6i + (3 * 3i + i * 3i)) = 0
(18 + 6i + (9i + 3i2)) = 0

Combine like terms: 6i + 9i = 15i
(18 + 15i + 3i2) = 0

Solving
18 + 15i + 3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 5i + i2) = 0

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

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

Simplifying
2 + i = 0

Solving
2 + i = 0

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

Add '-2' to each side of the equation.
2 + -2 + i = 0 + -2

Combine like terms: 2 + -2 = 0
0 + i = 0 + -2
i = 0 + -2

Combine like terms: 0 + -2 = -2
i = -2

Simplifying
i = -2
Solution
i = {-3, -2}