(x+3)(x+21)=0

Solution for (x+3)(x+21)=0 equation:

(x+3)(x+21)=0

We multiply parentheses ..

(+x^2+21x+3x+63)=0

We get rid of parentheses

x^2+21x+3x+63=0

We add all the numbers together, and all the variables

x^2+24x+63=0

a = 1; b = 24; c = +63;
Δ = b2-4ac
Δ = 242-4·1·63
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18}{2*1}=\frac{-42}{2}
=-21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18}{2*1}=\frac{-6}{2}
=-3
$