4i(-i+3)-3(6-2i)=

Solution for 4i(-i+3)-3(6-2i)= equation:

Simplifying
4i(-1i + 3) + -3(6 + -2i) = 0

Reorder the terms:
4i(3 + -1i) + -3(6 + -2i) = 0
(3 * 4i + -1i * 4i) + -3(6 + -2i) = 0
(12i + -4i2) + -3(6 + -2i) = 0
12i + -4i2 + (6 * -3 + -2i * -3) = 0
12i + -4i2 + (-18 + 6i) = 0

Reorder the terms:
-18 + 12i + 6i + -4i2 = 0

Combine like terms: 12i + 6i = 18i
-18 + 18i + -4i2 = 0

Solving
-18 + 18i + -4i2 = 0

Solving for variable 'i'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 9i + -2i2) = 0

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

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

Simplifying
-3 + i = 0

Solving
-3 + i = 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 + i = 0 + 3

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

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

Simplifying
i = 3
Subproblem 2
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
Solution
i = {3, 1.5}