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

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

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

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

Combine like terms: 3i + -18i = -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 + -1i2) = 0

Factor a trinomial.
3((1 + -1i)(6 + i)) = 0

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

Simplifying
1 + -1i = 0

Solving
1 + -1i = 0

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

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

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

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

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

Simplifying
i = 1
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 = {1, -6}