(6+z)(5z+7)=0

Solution for (6+z)(5z+7)=0 equation:

(6+z)(5z+7)=0

We add all the numbers together, and all the variables

(z+6)(5z+7)=0

We multiply parentheses ..

(+5z^2+7z+30z+42)=0

We get rid of parentheses

5z^2+7z+30z+42=0

We add all the numbers together, and all the variables

5z^2+37z+42=0

a = 5; b = 37; c = +42;
Δ = b2-4ac
Δ = 372-4·5·42
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-23}{2*5}=\frac{-60}{10}
=-6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+23}{2*5}=\frac{-14}{10}
=-1+2/5
$