(3-3i)(3+i)=

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

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

Multiply (3 + -3i) * (3 + i)
(3(3 + i) + -3i * (3 + i)) = 0
((3 * 3 + i * 3) + -3i * (3 + i)) = 0
((9 + 3i) + -3i * (3 + i)) = 0
(9 + 3i + (3 * -3i + i * -3i)) = 0
(9 + 3i + (-9i + -3i2)) = 0

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

Solving
9 + -6i + -3i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -2i + -1i2) = 0

Factor a trinomial.
3((1 + -1i)(3 + 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 '(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 = {1, -3}