(6+z)(3z+7)=0

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

(6+z)(3z+7)=0

We add all the numbers together, and all the variables

(z+6)(3z+7)=0

We multiply parentheses ..

(+3z^2+7z+18z+42)=0

We get rid of parentheses

3z^2+7z+18z+42=0

We add all the numbers together, and all the variables

3z^2+25z+42=0

a = 3; b = 25; c = +42;
Δ = b2-4ac
Δ = 252-4·3·42
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-11}{2*3}=\frac{-36}{6}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+11}{2*3}=\frac{-14}{6}
=-2+1/3
$