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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+21x^2+18x+14x+12)=0

We get rid of parentheses

21x^2+18x+14x+12=0

We add all the numbers together, and all the variables

21x^2+32x+12=0

a = 21; b = 32; c = +12;
Δ = b2-4ac
Δ = 322-4·21·12
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4}{2*21}=\frac{-36}{42}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4}{2*21}=\frac{-28}{42}
=-2/3
$