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x\left(5x+4\right)\geq 0
Factor out x.
x+\frac{4}{5}\leq 0 x\leq 0
For the product to be ≥0, x+\frac{4}{5} and x have to be both ≤0 or both ≥0. Consider the case when x+\frac{4}{5} and x are both ≤0.
x\leq -\frac{4}{5}
The solution satisfying both inequalities is x\leq -\frac{4}{5}.
x\geq 0 x+\frac{4}{5}\geq 0
Consider the case when x+\frac{4}{5} and x are both ≥0.
x\geq 0
The solution satisfying both inequalities is x\geq 0.
x\leq -\frac{4}{5}\text{; }x\geq 0
The final solution is the union of the obtained solutions.