(6z+10)(7z-6)=0

Solution for (6z+10)(7z-6)=0 equation:

(6z+10)(7z-6)=0

We multiply parentheses ..

(+42z^2-36z+70z-60)=0

We get rid of parentheses

42z^2-36z+70z-60=0

We add all the numbers together, and all the variables

42z^2+34z-60=0

a = 42; b = 34; c = -60;
Δ = b2-4ac
Δ = 342-4·42·(-60)
Δ = 11236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11236}=106$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-106}{2*42}=\frac{-140}{84}
=-1+2/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+106}{2*42}=\frac{72}{84}
=6/7
$