Factorize the equation: $a^{2}+4 a-21$

Step 1 ：Given the equation \(a^{2}+4 a-21\).

Step 2 ：We need to find two numbers that add up to 4 and multiply to -21.

Step 3 ：The two numbers that satisfy these conditions are 7 and -3 because 7 + (-3) = 4 and 7 * (-3) = -21.

Step 4 ：Now, we can rewrite the given equation in its factorized form.

Step 5 ：The factorized form of the equation is \((a - 3)(a + 7) = 0\).

Step 6 ：Final Answer: The factorized form of the equation \(a^{2}+4 a-21\) is \(\boxed{(a - 3)(a + 7) = 0}\).