(6x+3)(7x+2)=0

Solution for (6x+3)(7x+2)=0 equation:

(6x+3)(7x+2)=0

We multiply parentheses ..

(+42x^2+12x+21x+6)=0

We get rid of parentheses

42x^2+12x+21x+6=0

We add all the numbers together, and all the variables

42x^2+33x+6=0

a = 42; b = 33; c = +6;
Δ = b2-4ac
Δ = 332-4·42·6
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-9}{2*42}=\frac{-42}{84}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+9}{2*42}=\frac{-24}{84}
=-2/7
$