(2x+6)(-9x-7)-(2x+6)(8x+4)=0

Solution for (2x+6)(-9x-7)-(2x+6)(8x+4)=0 equation:

(2x+6)(-9x-7)-(2x+6)(8x+4)=0

We multiply parentheses ..

(-18x^2-14x-54x-42)-(2x+6)(8x+4)=0

We get rid of parentheses

-18x^2-14x-54x-(2x+6)(8x+4)-42=0

We multiply parentheses ..

-18x^2-(+16x^2+8x+48x+24)-14x-54x-42=0

We add all the numbers together, and all the variables

-18x^2-(+16x^2+8x+48x+24)-68x-42=0

We get rid of parentheses

-18x^2-16x^2-8x-48x-68x-24-42=0

We add all the numbers together, and all the variables

-34x^2-124x-66=0

a = -34; b = -124; c = -66;
Δ = b2-4ac
Δ = -1242-4·(-34)·(-66)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-80}{2*-34}=\frac{44}{-68}
=-11/17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+80}{2*-34}=\frac{204}{-68}
=-3
$