3(3-2i)(4+i)=0

Solution for 3(3-2i)(4+i)=0 equation:

Simplifying
3(3 + -2i)(4 + i) = 0

Multiply (3 + -2i) * (4 + i)
3(3(4 + i) + -2i * (4 + i)) = 0
3((4 * 3 + i * 3) + -2i * (4 + i)) = 0
3((12 + 3i) + -2i * (4 + i)) = 0
3(12 + 3i + (4 * -2i + i * -2i)) = 0
3(12 + 3i + (-8i + -2i2)) = 0

Combine like terms: 3i + -8i = -5i
3(12 + -5i + -2i2) = 0
(12 * 3 + -5i * 3 + -2i2 * 3) = 0
(36 + -15i + -6i2) = 0

Solving
36 + -15i + -6i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + -5i + -2i2) = 0

Factor a trinomial.
3((3 + -2i)(4 + i)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -2i)' equal to zero and attempt to solve:

Simplifying
3 + -2i = 0

Solving
3 + -2i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2i = 0 + -3
-2i = 0 + -3

Combine like terms: 0 + -3 = -3
-2i = -3

Divide each side by '-2'.
i = 1.5

Simplifying
i = 1.5
Subproblem 2
Set the factor '(4 + i)' equal to zero and attempt to solve:

Simplifying
4 + i = 0

Solving
4 + i = 0

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

Add '-4' to each side of the equation.
4 + -4 + i = 0 + -4

Combine like terms: 4 + -4 = 0
0 + i = 0 + -4
i = 0 + -4

Combine like terms: 0 + -4 = -4
i = -4

Simplifying
i = -4
Solution
i = {1.5, -4}