how to solve 3[x-(- 1/3+2i�ã14/3)][x-(-1/3-2i�ã14/3)]

To solve the expression 3[x-(-1/3+2i�ã14/3)][x-(-1/3-2i�ã14/3)], you can follow these steps:

Step 1: Simplify the inner expressions inside the square brackets.

Inside the first square brackets:
- Distribute the negative sign: -(-1/3+2i�ã14/3) becomes 1/3-2i�ã14/3.
Inside the second square brackets:
- Distribute the negative sign: -(-1/3-2i�ã14/3) becomes 1/3+2i�ã14/3.

Now the expression becomes:
3[x-(1/3-2i�ã14/3)][x-(1/3+2i�ã14/3)]

Step 2: Simplify further by multiplying the factors.

Multiply the two factors within each square bracket separately:
[x-(1/3-2i�ã14/3)] * [x-(1/3+2i�ã14/3)]

To multiply these factors, you can use the distributive property:
(x * x) - (x * (1/3+2i�ã14/3)) - ((1/3-2i�ã14/3) * x) + (1/3-2i�ã14/3) * (1/3+2i�ã14/3)

Step 3: Simplify the multiplication.

(x * x) simplifies to x^2.

To simplify the next terms, you need to multiply complex numbers:
- (x * (1/3+2i�ã14/3)) = (1/3)x + (2i�ã14/3)x
- ((1/3-2i�ã14/3) * x) = (1/3)x - (2i�ã14/3)x
- (1/3-2i�ã14/3) * (1/3+2i�ã14/3) is a multiplication of complex conjugates, which results in real numbers only. The product is (1/9 + 4).

Now, the expression becomes:
x^2 - (1/3)x - (2i�ã14/3)x + (1/3)x - (2i�ã14/3)x + (1/9 + 4)

Simplifying further:
x^2 - (1/3)x + (1/3)x - (2i�ã14/3)x - (2i�ã14/3)x + (1/9 + 4)

Combine like terms:
x^2 + (5/9) - (4i�ã14/3)x - (4i�ã14/3)x + (1/9 + 4)

Simplify the constants:
x^2 + (14/9) - (8i�ã14/3)x

Therefore, the solution to the expression 3[x-(-1/3+2i�ã14/3)][x-(-1/3-2i�ã14/3)] is x^2 + (14/9) - (8i�ã14/3)x.