(6x-6)(7x+6)=0

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

(6x-6)(7x+6)=0

We multiply parentheses ..

(+42x^2+36x-42x-36)=0

We get rid of parentheses

42x^2+36x-42x-36=0

We add all the numbers together, and all the variables

42x^2-6x-36=0

a = 42; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·42·(-36)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-78}{2*42}=\frac{-72}{84}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+78}{2*42}=\frac{84}{84}
=1
$