The only point of inflection on the curve representing the equation $$y=x^3+2x^2-10$$ is at:

Inflection points on a curve are points on the curve where the concavity changes. To find the inflection points of a curve we must find the points where the second derivative of the equation is equal to zero, $y^{\text{'}\text{'}}=0$.

We start by finding the first derivative $y^{\text{'}}$ as follows:

$y\text{'} = \frac{d }{dx}(x^3 + 2x^2 - 10)$

Remembering that the derivative of a constant is 0 and that the derivative a variable to the $n^{th}$ power is $\frac{d }{dx}{x}^n=n{x}^{n-1}$.

$y\text{'} = 3x^2 + 4x$

Now that we have the first derivative, we can start finding $y\text{'}\text{'}$ as follows:

$$\begin{gathered} y\text{'}\text{'} = \frac{d }{dx}(3x^2 + 4x) \\ = 6x +4 \end{gathered}$$

Setting $y\text{'}\text{'} = 0$ we find the inflection point as follows:

$$\begin{gathered} 0 = 6x + 4 \\ -4 = 6x \\ x = -\frac{4}{6}=-\frac{2}{3} \end{gathered}$$