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

Solution for (6+x)(21+3x)=0 equation:

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

We add all the numbers together, and all the variables

(x+6)(3x+21)=0

We multiply parentheses ..

(+3x^2+21x+18x+126)=0

We get rid of parentheses

3x^2+21x+18x+126=0

We add all the numbers together, and all the variables

3x^2+39x+126=0

a = 3; b = 39; c = +126;
Δ = b2-4ac
Δ = 392-4·3·126
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3}{2*3}=\frac{-42}{6}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3}{2*3}=\frac{-36}{6}
=-6
$