-2x^2*(2x+3)>0 — step-by-step solution

1) Let's solve in

ℝ

-2 x^{2} \cdot (2 x + 3) > 0

We study the sign of each factor of the product

⇥

x^{2}

is an even power: it is positive or zero and is zero only at

x = 0

⇥Its coefficient,

-2

, being negative, the expression

- 2 x^{2}

is zero at

x = 0

and negative otherwise

⇥The expression

2 x + 3

is zero at:

⇥

x = - \frac{3}{2}

⇥Its coefficient of

x

2

, being positive, it is negative before and positive after

- \frac{3}{2}

2) Let's draw up the sign table:

▶Solution found:

x < - \frac{3}{2}

3) The numeric value of:

x < - \frac{3}{2}

equals:

▷

x < -1.5