What is -x^3+6x^2+4x>24 ?

The solution to -x^3+6x^2+4x>24 is x<-2\lor 2<x<6

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-x^3+6x^2+4x>24

- x^{3} + 6 x^{2} + 4 x > 24

x < - 2 or 2 < x < 6

Interval Notation

(- \infty, - 2) \cup (2, 6)

Solution steps

- x^{3} + 6 x^{2} + 4 x > 24

Rewrite in standard form

- x^{3} + 6 x^{2} + 4 x - 24 > 0

Factor

- x^{3} + 6 x^{2} + 4 x - 24 : - (x - 6) (x + 2) (x - 2)

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

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 6) (x + 2) (x - 2)) (- 1) < 0 \cdot (- 1)

Simplify

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

Identify the intervals

x < - 2 or 2 < x < 6

3 y = - 12

4 m^{2} + 16 mn - 7 m - 28 n

8 x^{2} y (- 13 x y^{3})

2 + x > 16

8 x + 3 \geq 19