(3+5i)(6-6i)=

Solution for (3+5i)(6-6i)= equation:

Simplifying
(3 + 5i)(6 + -6i) = 0

Multiply (3 + 5i) * (6 + -6i)
(3(6 + -6i) + 5i * (6 + -6i)) = 0
((6 * 3 + -6i * 3) + 5i * (6 + -6i)) = 0
((18 + -18i) + 5i * (6 + -6i)) = 0
(18 + -18i + (6 * 5i + -6i * 5i)) = 0
(18 + -18i + (30i + -30i2)) = 0

Combine like terms: -18i + 30i = 12i
(18 + 12i + -30i2) = 0

Solving
18 + 12i + -30i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + 2i + -5i2) = 0

Factor a trinomial.
6((1 + -1i)(3 + 5i)) = 0

Ignore the factor 6.
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 + 5i)' equal to zero and attempt to solve:

Simplifying
3 + 5i = 0

Solving
3 + 5i = 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 + 5i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5i = 0 + -3
5i = 0 + -3

Combine like terms: 0 + -3 = -3
5i = -3

Divide each side by '5'.
i = -0.6

Simplifying
i = -0.6
Solution
i = {1, -0.6}