#### Answer

$x=-7~$ or $~x=3$

#### Work Step by Step

Let's consider a trinomial in this form: $~x^2+bx+c$
To factor this trinomial, we need to find two numbers $r$ and $s$ such that $r+s = b$ and $r\times s = c$
Then we can factor the trinomial as follows:
$~x^2+bx+c = (x+r)~(x+s)$
We can rewrite the given equation:
$x^2+4x=21$
$x^2+4x-21 = 0$
To factor the left side of the equation, we need to find two numbers $r$ and $s$ such that $r+s = 4$ and $r\times s = -21$. We can see that $(7)+(-3) = 4~$ and $(7)\times (-3) = -21$
We can solve the equation as follows:
$x^2+4x=21$
$x^2+4x-21 = 0$
$(x+7)(x-3)=0$
$x=-7~$ or $~x=3$