Factorise and find the value of x. Y= 2x^3 +2 ?

To factorise the given expression, we first need to factor out the common factor of 2:

Y = 2(x^3 + 1)

Now, we can see that the expression inside the parentheses is a sum of cubes, which can be factored using the formula a^3 + b^3 = (a + b)(a^2 - ab + b^2):

Y = 2(x + 1)(x^2 - x + 1)

To find the value of x, we set Y equal to 0 and solve for x:

0 = 2(x + 1)(x^2 - x + 1)

Either x + 1 = 0 or x^2 - x + 1 = 0

If x + 1 = 0, then x = -1

If x^2 - x + 1 = 0, we can use the quadratic formula to find the other two roots:

x = [1 ± sqrt(1 - 4(1)(1))]/2
x = [1 ± sqrt(-3)]/2
x = [1 ± i√3]/2

Therefore, the values of x are -1, [1 + i√3]/2, and [1 - i√3]/2.

The equation is not correct. Please provide the correct equation to factorise and find the value of x.