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

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

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

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

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

Solving
36 + 36i + 9i2 = 0

Solving for variable 'i'.

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

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

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

Simplifying
2 + i = 0

Solving
2 + i = 0

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

Add '-2' to each side of the equation.
2 + -2 + i = 0 + -2

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

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

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

Simplifying
2 + i = 0

Solving
2 + i = 0

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

Add '-2' to each side of the equation.
2 + -2 + i = 0 + -2

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

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

Simplifying
i = -2
Solution
i = {-2, -2}