(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 = 0
(36 + 0 + -9i2) = 0
(36 + -9i2) = 0

Solving
36 + -9i2 = 0

Solving for variable 'i'.

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

Add '-36' to each side of the equation.
36 + -36 + -9i2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -9i2 = 0 + -36
-9i2 = 0 + -36

Combine like terms: 0 + -36 = -36
-9i2 = -36

Divide each side by '-9'.
i2 = 4

Simplifying
i2 = 4

Take the square root of each side:
i = {-2, 2}