12x+192=(x+2)(x+12)

Solution for 12x+192=(x+2)(x+12) equation:

12x+192=(x+2)(x+12)

We move all terms to the left:

12x+192-((x+2)(x+12))=0

We multiply parentheses ..

-((+x^2+12x+2x+24))+12x+192=0


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

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

We get rid of parentheses

x^2+12x+2x+24

We add all the numbers together, and all the variables

x^2+14x+24

Back to the equation:

-(x^2+14x+24)


We add all the numbers together, and all the variables

12x-(x^2+14x+24)+192=0

We get rid of parentheses

-x^2+12x-14x-24+192=0

We add all the numbers together, and all the variables

-1x^2-2x+168=0

a = -1; b = -2; c = +168;
Δ = b2-4ac
Δ = -22-4·(-1)·168
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-26}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+26}{2*-1}=\frac{28}{-2}
=-14
$