What is -x^3+7x^2+9x>63 ?

The solution to -x^3+7x^2+9x>63 is x<-3\lor 3<x<7

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-x^3+7x^2+9x>63

- x^{3} + 7 x^{2} + 9 x > 63

x < - 3 or 3 < x < 7

Interval Notation

(- \infty, - 3) \cup (3, 7)

Solution steps

- x^{3} + 7 x^{2} + 9 x > 63

Rewrite in standard form

- x^{3} + 7 x^{2} + 9 x - 63 > 0

Factor

- x^{3} + 7 x^{2} + 9 x - 63 : - (x - 7) (x + 3) (x - 3)

- (x - 7) (x + 3) (x - 3) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 7) (x + 3) (x - 3)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 7) (x + 3) (x - 3) < 0

Identify the intervals

x < - 3 or 3 < x < 7

4 x^{2} - 24 x + 20 = 0

\frac{2 - 5}{2 + 5}

- 3 (z + 4)^{2} = - 108

\frac{9 ^{n}}{3 ^{2 n + 1}}

\frac{x}{3} > 4