12x+x=(4x+8)(3x-3)

Solution for 12x+x=(4x+8)(3x-3) equation:

12x+x=(4x+8)(3x-3)

We move all terms to the left:

12x+x-((4x+8)(3x-3))=0

We add all the numbers together, and all the variables

13x-((4x+8)(3x-3))=0

We multiply parentheses ..

-((+12x^2-12x+24x-24))+13x=0


We calculate terms in parentheses: -((+12x^2-12x+24x-24)), so:

(+12x^2-12x+24x-24)

We get rid of parentheses

12x^2-12x+24x-24

We add all the numbers together, and all the variables

12x^2+12x-24

Back to the equation:

-(12x^2+12x-24)


We add all the numbers together, and all the variables

13x-(12x^2+12x-24)=0

We get rid of parentheses

-12x^2+13x-12x+24=0

We add all the numbers together, and all the variables

-12x^2+x+24=0

a = -12; b = 1; c = +24;
Δ = b2-4ac
Δ = 12-4·(-12)·24
Δ = 1153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1153}}{2*-12}=\frac{-1-\sqrt{1153}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1153}}{2*-12}=\frac{-1+\sqrt{1153}}{-24}
$