2x²>=-4x

To solve this inequality, let's start by moving all the terms to one side of the inequality sign:

2x² + 4x ≥ 0

Now, let's factor out a common x from both terms:

x(2x + 4) ≥ 0

To find the values of x that satisfy the inequality, we need to consider two cases:

Case 1: x > 0

If x > 0, then both x and (2x + 4) are positive. In this case, the inequality holds true.

Case 2: x < 0

If x < 0, then x is negative and (2x + 4) is positive. In this case, the inequality does not hold true.

Now, let's consider when x = 0. Substituting x = 0 into the inequality:

2(0)² + 4(0) ≥ 0 0 ≥ 0

When x = 0, the inequality holds true.

Therefore, the solutions to the inequality 2x² + 4x ≥ 0 are x ≥ 0.