(-6x+2)(-9x-3)-(-x+4)(-9x-3)=0

Solution for (-6x+2)(-9x-3)-(-x+4)(-9x-3)=0 equation:

(-6x+2)(-9x-3)-(-x+4)(-9x-3)=0

We add all the numbers together, and all the variables

(-6x+2)(-9x-3)-(-1x+4)(-9x-3)=0

We multiply parentheses ..

(+54x^2+18x-18x-6)-(-1x+4)(-9x-3)=0

We get rid of parentheses

54x^2+18x-18x-(-1x+4)(-9x-3)-6=0

We multiply parentheses ..

54x^2-(+9x^2+3x-36x-12)+18x-18x-6=0

We add all the numbers together, and all the variables

54x^2-(+9x^2+3x-36x-12)-6=0

We get rid of parentheses

54x^2-9x^2-3x+36x+12-6=0

We add all the numbers together, and all the variables

45x^2+33x+6=0

a = 45; b = 33; c = +6;
Δ = b2-4ac
Δ = 332-4·45·6
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3}{2*45}=\frac{-36}{90}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3}{2*45}=\frac{-30}{90}
=-1/3
$