What is x+6x+6x^2+6x+5<0 ?

The solution to x+6x+6x^2+6x+5<0 is -5/3 <x<-1/2

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x+6x+6x^2+6x+5<0

x + 6 x + 6 x^{2} + 6 x + 5 < 0

- \frac{5}{3} < x < - \frac{1}{2}

Interval Notation

(- \frac{5}{3}, - \frac{1}{2})

Decimal Notation

- 1.66666 \dots < x < - 0.5

Solution steps

x + 6 x + 6 x^{2} + 6 x + 5 < 0

Rewrite in standard form

6 x^{2} + 13 x + 5 < 0

Factor

6 x^{2} + 13 x + 5 : (2 x + 1) (3 x + 5)

(2 x + 1) (3 x + 5) < 0

Identify the intervals

- \frac{5}{3} < x < - \frac{1}{2}

\frac{1}{x ^{2} - 1} \geq 0

\frac{( ( x ^{2} - 11 x + 24 ) ^{101} )}{( ( x ^{2} - 10 x + 24 ) ^{100} )} \leq 0

- 3 x^{2} + 8 x + 35 > 0

\frac{4}{( 3 x + 2 )} \geq 0

2 x^{2} - 7 x + 7 > 0