\[ x^{2}+9 x=-20 \] Factored Form Real Number Solutions

Step 1 ：Rearrange the equation into a standard quadratic form, which is \(ax^2 + bx + c = 0\). The equation is \(x^{2}+9 x+20=0\).

Step 2 ：Use the quadratic formula to find the solutions. The quadratic formula is \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 3 ：Substitute a = 1, b = 9, c = 20 into the quadratic formula to get the solutions.

Step 4 ：The solutions to the equation are \(x = -4\) and \(x = -5\). These are the real number solutions.

Step 5 ：Obtain the factored form of the equation by setting the equation to zero and factoring the quadratic expression.

Step 6 ：The factored form of the equation is \((x + 5)(x + 4) = 0\).

Step 7 ：Final Answer: The factored form of the equation is \(\boxed{(x + 5)(x + 4) = 0}\) and the real number solutions are \(\boxed{x = -4}\) and \(\boxed{x = -5}\).