What is x(x-2)(-2x+6)<0 ?

The solution to x(x-2)(-2x+6) 3

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x(x-2)(-2x+6)<0

x (x - 2) (- 2 x + 6) < 0

0 < x < 2 or x > 3

Interval Notation

(0, 2) \cup (3, \infty)

Solution steps

x (x - 2) (- 2 x + 6) < 0

Rewrite in standard form

- x^{3} + 5 x^{2} - 6 x < 0

Factor

- x^{3} + 5 x^{2} - 6 x : - x (x - 2) (x - 3)

- x (x - 2) (x - 3) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x - 2) (x - 3)) (- 1) > 0 \cdot (- 1)

Simplify

x (x - 2) (x - 3) > 0

Identify the intervals

0 < x < 2 or x > 3

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

(2 x + 5)^{2} < (5 x + 2)^{2}

2 x - x^{2} - 15 < 0

3 x - 10 x - 2 x^{2} < 0

x^{3} - 7 x + 6 \geq 0