Integrate the gradient function.

The gradient function of the curve is given by $\frac{dy}{dx} = 3 - 4x$.
To find the equation of the curve, we integrate $\frac{dy}{dx}$ with respect to $x$:

$$y = \int (3 - 4x) \, dx$$ $$y = 3x - \frac{4x^2}{2} + C$$ $$y = 3x - 2x^2 + C$$

The curve passes through the point $(-1, 10)$. Substitute $x = -1$ and $y = 10$ into the equation:

$$10 = 3(-1) - 2(-1)^2 + C$$ $$10 = -3 - 2(1) + C$$ $$10 = -3 - 2 + C$$ $$10 = -5 + C$$ $$C = 10 + 5$$ $$C = 15$$

Substitute the value of $C$ back into the equation from Step 1:

$$y = 3x - 2x^2 + 15$$

The equation of the curve is $y = -2x^2 + 3x + 15$.