Solve (169+13x+x^2)(x-13)-x^3-2262x<0

$$( 169 + 13 x + x ^ { 2 } ) ( x - 13 ) - x ^ { 3 } - 2262 x < 0$$

Solve for x

$$x>-\frac{169}{174}$$

Solution Steps

Use the distributive property to multiply 169+13x+x^{2} by x-13 and combine like terms.

$$-2197+x^{3}-x^{3}-2262x<0$$

Combine x^{3} and -x^{3} to get 0.

$$-2197-2262x<0$$

Add 2197 to both sides. Anything plus zero gives itself.

$$-2262x<2197$$

Divide both sides by -2262. Since -2262 is negative, the inequality direction is changed.

$$x>\frac{2197}{-2262}$$

Reduce the fraction \frac{2197}{-2262} to lowest terms by extracting and canceling out 13.

$$x>-\frac{169}{174}$$