(2x+6)(3x-21)=0

Solution for (2x+6)(3x-21)=0 equation:

(2x+6)(3x-21)=0

We multiply parentheses ..

(+6x^2-42x+18x-126)=0

We get rid of parentheses

6x^2-42x+18x-126=0

We add all the numbers together, and all the variables

6x^2-24x-126=0

a = 6; b = -24; c = -126;
Δ = b2-4ac
Δ = -242-4·6·(-126)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-60}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+60}{2*6}=\frac{84}{12}
=7
$