What is (x-3)^2(12-3x)>0 ?

The solution to (x-3)^2(12-3x)>0 is x<3\lor 3<x<4

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(x-3)^2(12-3x)>0

(x - 3)^{2} (12 - 3 x) > 0

x < 3 or 3 < x < 4

Interval Notation

(- \infty, 3) \cup (3, 4)

Solution steps

(x - 3)^{2} (12 - 3 x) > 0

Rewrite in standard form

- x^{3} + 10 x^{2} - 33 x + 36 > 0

Factor

- x^{3} + 10 x^{2} - 33 x + 36 : - (x - 3)^{2} (x - 4)

- (x - 3)^{2} (x - 4) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 3)^{2} (x - 4)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 3)^{2} (x - 4) < 0

Identify the intervals

x < 3 or 3 < x < 4

\frac{8 ^{- 6}}{4 ^{- 6}}

0 < \frac{1}{3} x < π

x^{2} - 2 x = 0

\frac{b + 11}{3} = - 2

(5 - 3) (5 + 23)