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

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

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

Multiply (3 + 6i) * (3 + 6i)
(3(3 + 6i) + 6i * (3 + 6i)) = 0
((3 * 3 + 6i * 3) + 6i * (3 + 6i)) = 0
((9 + 18i) + 6i * (3 + 6i)) = 0
(9 + 18i + (3 * 6i + 6i * 6i)) = 0
(9 + 18i + (18i + 36i2)) = 0

Combine like terms: 18i + 18i = 36i
(9 + 36i + 36i2) = 0

Solving
9 + 36i + 36i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '9'.
9(1 + 4i + 4i2) = 0

Factor a trinomial.
9((1 + 2i)(1 + 2i)) = 0

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

Simplifying
1 + 2i = 0

Solving
1 + 2i = 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 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve:

Simplifying
1 + 2i = 0

Solving
1 + 2i = 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 + 2i = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2i = 0 + -1
2i = 0 + -1

Combine like terms: 0 + -1 = -1
2i = -1

Divide each side by '2'.
i = -0.5

Simplifying
i = -0.5
Solution
i = {-0.5, -0.5}