2x²>=-4x

To solve the inequality 2x² >= -4x, we can start by bringing all terms to one side of the inequality:

2x² + 4x >= 0

Next, we can factor out a common factor of 2x:

2x(x + 2) >= 0

Now, we can determine the values of x that satisfy the inequality by considering the signs of each factor separately.

For 2x to be positive or zero, x must be greater than or equal to 0.

For (x + 2) to be positive or zero, x must be greater than or equal to -2.

In order for both factors to be positive or zero, x must be greater than or equal to 0.

Therefore, the solution to the inequality 2x² >= -4x is x >= 0.