Solve for x
x\in \left(0,4\right)
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-2x^{2}+8x>0
Use the distributive property to multiply -2x by x-4.
2x^{2}-8x<0
Multiply the inequality by -1 to make the coefficient of the highest power in -2x^{2}+8x positive. Since -1 is negative, the inequality direction is changed.
2x\left(x-4\right)<0
Factor out x.
x>0 x-4<0
For the product to be negative, x and x-4 have to be of the opposite signs. Consider the case when x is positive and x-4 is negative.
x\in \left(0,4\right)
The solution satisfying both inequalities is x\in \left(0,4\right).
x-4>0 x<0
Consider the case when x-4 is positive and x is negative.
x\in \emptyset
This is false for any x.
x\in \left(0,4\right)
The final solution is the union of the obtained solutions.
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