(12-4i)(3+i)=0

Solution for (12-4i)(3+i)=0 equation:

Simplifying
(12 + -4i)(3 + i) = 0

Multiply (12 + -4i) * (3 + i)
(12(3 + i) + -4i * (3 + i)) = 0
((3 * 12 + i * 12) + -4i * (3 + i)) = 0
((36 + 12i) + -4i * (3 + i)) = 0
(36 + 12i + (3 * -4i + i * -4i)) = 0
(36 + 12i + (-12i + -4i2)) = 0

Combine like terms: 12i + -12i = 0
(36 + 0 + -4i2) = 0
(36 + -4i2) = 0

Solving
36 + -4i2 = 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 + -4i2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -4i2 = 0 + -36
-4i2 = 0 + -36

Combine like terms: 0 + -36 = -36
-4i2 = -36

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

Simplifying
i2 = 9

Take the square root of each side:
i = {-3, 3}