(12*12)=(x*x)+((x+6)(x+6))

Solution for (12*12)=(x*x)+((x+6)(x+6)) equation:

(12*12)=(x*x)+((x+6)(x+6))

We move all terms to the left:

(12*12)-((x*x)+((x+6)(x+6)))=0

We add all the numbers together, and all the variables

-((+x*x)+((x+6)(x+6)))+144=0

We multiply parentheses ..

-((+x*x)+((+x^2+6x+6x+36)))+144=0


We calculate terms in parentheses: -((+x*x)+((+x^2+6x+6x+36))), so:

(+x*x)+((+x^2+6x+6x+36))

determiningTheFunctionDomain
((+x^2+6x+6x+36))+(+x*x)

We get rid of parentheses

((+x^2+6x+6x+36))+x*x


We calculate terms in parentheses: +((+x^2+6x+6x+36)), so:

(+x^2+6x+6x+36)

We get rid of parentheses

x^2+6x+6x+36

We add all the numbers together, and all the variables

x^2+12x+36

Back to the equation:

+(x^2+12x+36)


Wy multiply elements

x^2+(x^2+12x+36)

We get rid of parentheses

x^2+x^2+12x+36

We add all the numbers together, and all the variables

2x^2+12x+36

Back to the equation:

-(2x^2+12x+36)


We get rid of parentheses

-2x^2-12x-36+144=0

We add all the numbers together, and all the variables

-2x^2-12x+108=0

a = -2; b = -12; c = +108;
Δ = b2-4ac
Δ = -122-4·(-2)·108
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*-2}=\frac{12-12\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*-2}=\frac{12+12\sqrt{7}}{-4}
$