Solve the following equation. \[ c^{2}+2 c-15=0 \]

Step 1 ：Given the quadratic equation \(c^{2}+2 c-15=0\)

Step 2 ：This equation is in the form of \(ax^2 + bx + c = 0\)

Step 3 ：The solutions to a quadratic equation can be found using the quadratic formula, which is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 4 ：In this case, \(a = 1\), \(b = 2\), and \(c = -15\)

Step 5 ：We can substitute these values into the quadratic formula to find the solutions

Step 6 ：Calculate the discriminant \(D = b^2 - 4ac = 64\)

Step 7 ：Find the roots of the equation \(x1 = -5.0\) and \(x2 = 3.0\)

Step 8 ：The solutions to the equation are \(c = \boxed{-5.0}\) and \(c = \boxed{3.0}\)