What is (x-6)^2(28-4x)>0 ?

The solution to (x-6)^2(28-4x)>0 is x<6\lor 6<x<7

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(x-6)^2(28-4x)>0

(x - 6)^{2} (28 - 4 x) > 0

x < 6 or 6 < x < 7

Interval Notation

(- \infty, 6) \cup (6, 7)

Solution steps

(x - 6)^{2} (28 - 4 x) > 0

Rewrite in standard form

- x^{3} + 19 x^{2} - 120 x + 252 > 0

Factor

- x^{3} + 19 x^{2} - 120 x + 252 : - (x - 6)^{2} (x - 7)

- (x - 6)^{2} (x - 7) > 0

Multiply both sides by

- 1

(reverse the inequality)

(- (x - 6)^{2} (x - 7)) (- 1) < 0 \cdot (- 1)

Simplify

(x - 6)^{2} (x - 7) < 0

Identify the intervals

x < 6 or 6 < x < 7

2 x + 13 < 3

\frac{1 ( 1 - ( \frac{1}{5} ) ^{6} )}{1 - \frac{1}{5}}

2 x = - 2

\frac{5}{2} = \frac{d - 2}{4}

\frac{- 7}{2}