What is (x^2-2x)(2x-2)-92x-2x^3-2x<0 ?

The solution to (x^2-2x)(2x-2)-92x-2x^3-2x 0

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(x^2-2x)(2x-2)-92x-2x^3-2x<0

(x^{2} - 2 x) (2 x - 2) - 92 x - 2 x^{3} - 2 x < 0

x < - 15 or x > 0

Interval Notation

(- \infty, - 15) \cup (0, \infty)

Solution steps

(x^{2} - 2 x) (2 x - 2) - 92 x - 2 x^{3} - 2 x < 0

Rewrite in standard form

- x^{2} - 15 x < 0

Factor

- x^{2} - 15 x : - x (x + 15)

- x (x + 15) < 0

Multiply both sides by

- 1

(reverse the inequality)

(- x (x + 15)) (- 1) > 0 \cdot (- 1)

Simplify

x (x + 15) > 0

Identify the intervals

x < - 15 or x > 0

2 x^{2} + 5 > 4

x^{2} - x - 10 > - 10

x^{2} + 5 x + 12 > 0

\frac{x ^{2} - 7 x + 12}{2 x ^{2} + 4 x + 5} > \frac{1}{2}

\frac{4}{( x - 3 )} < 0

What is (x^2-2x)(2x-2)-92x-2x^3-2x<0 ?
The solution to (x^2-2x)(2x-2)-92x-2x^3-2x<0 is x<-15\lor x>0