Find the equation of the normals to the curve y = x³ + 2x + 6 which are parallel to line x + 14y + 4 = 0.

The equation of the given curve is y = x³ + 2x + 6. The slope of the tangent to the given curve at any point (x, y) is given by, -1 < x < 1

∴ Slope of the normal to the given curve at any point (x, y) = x² < 1

The equation of the given line is x + 14y + 4 = 0.