What is x(x+6)*(x+2)^2*(x-3)>0 ?

The solution to x(x+6)*(x+2)^2*(x-3)>0 is -6 3

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x(x+6)(x+2)^2(x-3)>0

x (x + 6) \cdot (x + 2)^{2} \cdot (x - 3) > 0

- 6 < x < - 2 or - 2 < x < 0 or x > 3

Interval Notation

(- 6, - 2) \cup (- 2, 0) \cup (3, \infty)

Solution steps

x (x + 6) (x + 2)^{2} (x - 3) > 0

Identify the intervals

- 6 < x < - 2 or - 2 < x < 0 or x > 3

\frac{1}{x} > \frac{1}{x} + 1

(x^{2} + 1) (x - 1) (x - 2) < 0

\frac{1}{( x - 1 )} - \frac{1}{( x - 2 )} + \frac{1}{( x - 3 )} > 0

\frac{( x - 2 ) ^{2}}{( x - 1 )} < 0

\frac{( x ^{2} + 6 x + 4 )}{( 3 x ^{2} - 9 x + 4 )} \leq 0

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