To find the points of intersection, set the equations equal: \(2x + 3 = cx^2 + 3x - c\).

Rearrange to form a quadratic equation: \(cx^2 + (3 - 2c)x - (c + 3) = 0\).

The discriminant of a quadratic \(ax^2 + bx + c = 0\) is given by \(b^2 - 4ac\).

Here, \(a = c\), \(b = 3 - 2c\), and \(c = -(c + 3)\).

Calculate the discriminant: \((3 - 2c)^2 - 4c(-c - 3)\).

Simplify: \((3 - 2c)^2 + 4c(c + 3) = 9 - 12c + 4c^2 + 4c^2 + 12c = 8c^2 + 9\).

The discriminant \(8c^2 + 9\) is always positive for all values of \(c\), indicating two real roots.

Thus, the line and curve intersect for all values of \(c\).