What is -8x^3-30x^2-18x<0 ?

The solution to -8x^3-30x^2-18x 0

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-8x^3-30x^2-18x<0

- 8 x^{3} - 30 x^{2} - 18 x < 0

- 3 < x < - \frac{3}{4} or x > 0

Interval Notation

(- 3, - \frac{3}{4}) \cup (0, \infty)

Decimal Notation

- 3 < x < - 0.75 or x > 0

Solution steps

- 8 x^{3} - 30 x^{2} - 18 x < 0

Rewrite in standard form

- 4 x^{3} - 15 x^{2} - 9 x < 0

Factor

- 4 x^{3} - 15 x^{2} - 9 x : - x (4 x + 3) (x + 3)

- x (4 x + 3) (x + 3) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (4 x + 3) (x + 3)) (- 1) > 0 \cdot (- 1)

Simplify

x (4 x + 3) (x + 3) > 0

Identify the intervals

- 3 < x < - \frac{3}{4} or x > 0

∣ x - 2 ∣ > 0

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

- 2 (\frac{1}{2})^{- 1}

- 7 x < 21

2 x^{3} - 12 x^{2} y - 14 x y^{2}

What is -8x^3-30x^2-18x<0 ?
The solution to -8x^3-30x^2-18x<0 is -3<x<-3/4 \lor x>0