What is (x^2-5x+6)*(-x^2-5x-4)>0 ?

The solution to (x^2-5x+6)*(-x^2-5x-4)>0 is -4<x<-1\lor 2<x<3

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(x^2-5x+6)*(-x^2-5x-4)>0

(x^{2} - 5 x + 6) \cdot (- x^{2} - 5 x - 4) > 0

- 4 < x < - 1 or 2 < x < 3

Interval Notation

(- 4, - 1) \cup (2, 3)

Solution steps

(x^{2} - 5 x + 6) (- x^{2} - 5 x - 4) > 0

Factor

(x^{2} - 5 x + 6) (- x^{2} - 5 x - 4) : - (x - 2) (x - 3) (x + 1) (x + 4)

- (x - 2) (x - 3) (x + 1) (x + 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 2) (x - 3) (x + 1) (x + 4)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 2) (x - 3) (x + 1) (x + 4) < 0

Identify the intervals

- 4 < x < - 1 or 2 < x < 3

x^{2} - 6 x - 21 = 0

\frac{x}{x - 5} < 0

p^{2} + 2 pq - 15 q^{2}

- \frac{1}{2} + \frac{5}{8}

3 (x + 4)^{2} = - 27

What is (x^2-5x+6)*(-x^2-5x-4)>0 ?
The solution to (x^2-5x+6)*(-x^2-5x-4)>0 is -4<x<-1\lor 2<x<3