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First, we need to set each factor equal to zero:
-2x = 0 and 5x - 2 = 0
Now, solve each equation separately:
-2x = 0
x = 0
5x - 2 = 0
5x = 2
x = 2/5
Therefore, the solutions to the equation -2x(5x - 2) = 0 are x = 0 and x = 2/5.