(6+6i)x(6+6i)=

Solution for (6+6i)x(6+6i)= equation:

Simplifying
(6 + 6i) * x(6 + 6i) = 0

Reorder the terms for easier multiplication:
x(6 + 6i)(6 + 6i) = 0

Multiply (6 + 6i) * (6 + 6i)
x(6(6 + 6i) + 6i * (6 + 6i)) = 0
x((6 * 6 + 6i * 6) + 6i * (6 + 6i)) = 0
x((36 + 36i) + 6i * (6 + 6i)) = 0
x(36 + 36i + (6 * 6i + 6i * 6i)) = 0
x(36 + 36i + (36i + 36i2)) = 0

Combine like terms: 36i + 36i = 72i
x(36 + 72i + 36i2) = 0
(36 * x + 72i * x + 36i2 * x) = 0

Reorder the terms:
(72ix + 36i2x + 36x) = 0
(72ix + 36i2x + 36x) = 0

Solving
72ix + 36i2x + 36x = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '36x'.
36x(2i + i2 + 1) = 0

Factor a trinomial.
36x((i + 1)(i + 1)) = 0

Ignore the factor 36.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(i + 1)' equal to zero and attempt to solve:

Simplifying
i + 1 = 0

Reorder the terms:
1 + i = 0

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

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

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

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

Simplifying
i + 1 = 0

Reorder the terms:
1 + i = 0

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

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

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

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