3x^2+9x<0 — step-by-step solution

1) Let's solve in

ℝ

3 x^{2} + 9 x < 0

You can factor:

3 x^{2} + 9 x

into:

x \cdot (3 x + 9)

We study the sign of each factor of the product

⇥The expression

x

is zero at

x = 0

, it is negative before and positive after

⇥The expression

3 x + 9

is zero at:

⇥

x = - \frac{9}{3}

⇥ⓘ We simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

- \frac{9}{3}

-3

⇥

x = -3

⇥Its coefficient of

x

3

, being positive, it is negative before and positive after

-3

2) Let's draw up the sign table:

▶Solution found:

x \in (-3, 0)