What is -x^3+6x^2-12x+9<0 ?

The solution to -x^3+6x^2-12x+9 3

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-x^3+6x^2-12x+9<0

- x^{3} + 6 x^{2} - 12 x + 9 < 0

x > 3

Interval Notation

(3, \infty)

Solution steps

- x^{3} + 6 x^{2} - 12 x + 9 < 0

Factor

- x^{3} + 6 x^{2} - 12 x + 9 : - (x - 3) (x^{2} - 3 x + 3)

- (x - 3) (x^{2} - 3 x + 3) < 0

Multiply both sides by

- 1

(reverse the inequality)

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

Simplify

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

Identify the intervals

x > 3

3 t^{2} + 4 t + 8 = - 6 t

- 42 \geq 40 + 41 c

\frac{1}{e ^{- 2}}

\frac{5 a ^{7}}{10 a ^{3}}

6 g^{3} - 24 g^{2} + 24 g