What is -x^3+6x^2+9x>54 ?

The solution to -x^3+6x^2+9x>54 is x<-3\lor 3<x<6

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-x^3+6x^2+9x>54

- x^{3} + 6 x^{2} + 9 x > 54

x < - 3 or 3 < x < 6

Interval Notation

(- \infty, - 3) \cup (3, 6)

Solution steps

- x^{3} + 6 x^{2} + 9 x > 54

Rewrite in standard form

- x^{3} + 6 x^{2} + 9 x - 54 > 0

Factor

- x^{3} + 6 x^{2} + 9 x - 54 : - (x - 6) (x + 3) (x - 3)

- (x - 6) (x + 3) (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 6) (x + 3) (x - 3)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 6) (x + 3) (x - 3) < 0

Identify the intervals

x < - 3 or 3 < x < 6

2 x^{2} + x - 8

(x - 2)^{2} (24 - 4 x) > 0

- w - 2.5 (4 w + 3) \geq 5.25 w - 3.5 - w

(x - 2)^{2} - (3 - x)^{2} = 1

6 x + 7 = 3 x + 46