To solve the equation Sin(2x) + Cos(x) + 2Sin(x) = -1, we will first try to simplify the expression by using trigonometric identities.

Recall that Sin(2x) = 2Sin(x)Cos(x), so we can rewrite our equation as:

2Sin(x)Cos(x) + Cos(x) + 2Sin(x) = -1

Now, let's combine our trigonometric terms:

2Sin(x)Cos(x) + 2Sin(x) + Cos(x) = -1

Now, we can factor out the common factor of 2Sin(x) from the first two terms on the left side of the equation:

2Sin(x)(Cos(x) + 1) + Cos(x) = -1

Now, let's simplify the expression further:

2Sin(x)(Cos(x) + 1) + Cos(x) = -1
2Sin(x)Cos(x) + 2Sin(x) + Cos(x) = -1

Now, we have simplified our equation. To solve it, we need to find the values of x that satisfy this equation. This can be done by either graphing the equation or using a numerical method to find the values of x that satisfy the equation.