What is -x^3+3x^2-2x>0 ?

The solution to -x^3+3x^2-2x>0 is x<0\lor 1<x<2

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-x^3+3x^2-2x>0

- x^{3} + 3 x^{2} - 2 x > 0

x < 0 or 1 < x < 2

Interval Notation

(- \infty, 0) \cup (1, 2)

Solution steps

- x^{3} + 3 x^{2} - 2 x > 0

Factor

- x^{3} + 3 x^{2} - 2 x : - x (x - 1) (x - 2)

- x (x - 1) (x - 2) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x - 1) (x - 2)) (- 1) < 0 \cdot (- 1)

Simplify

x (x - 1) (x - 2) < 0

Identify the intervals

x < 0 or 1 < x < 2

\frac{1}{( x + 4 )} \leq \frac{- 1}{6}

\frac{( ( x - 4 ) ( x - 3 ) )}{( x - 3 )} \leq 0

\frac{( 14 x )}{( x + 1 )} - \frac{( 9 x - 30 )}{( x - 4 )} < 0

\frac{1}{( 3 x - 2 )} \leq \frac{1}{( 3 x + 4 )}

n^{5} - n^{3} < 0