2(6-3x)(9x+3)=(6x-12)(3-21x)

Solution for 2(6-3x)(9x+3)=(6x-12)(3-21x) equation:

2(6-3x)(9x+3)=(6x-12)(3-21x)

We move all terms to the left:

2(6-3x)(9x+3)-((6x-12)(3-21x))=0

We add all the numbers together, and all the variables

2(-3x+6)(9x+3)-((6x-12)(-21x+3))=0

We multiply parentheses ..

2(-27x^2-9x+54x+18)-((6x-12)(-21x+3))=0


We calculate terms in parentheses: -((6x-12)(-21x+3)), so:

(6x-12)(-21x+3)

We multiply parentheses ..

(-126x^2+18x+252x-36)

We get rid of parentheses

-126x^2+18x+252x-36

We add all the numbers together, and all the variables

-126x^2+270x-36

Back to the equation:

-(-126x^2+270x-36)


We multiply parentheses

-54x^2-(-126x^2+270x-36)-18x+108x+36=0

We get rid of parentheses

-54x^2+126x^2-270x-18x+108x+36+36=0

We add all the numbers together, and all the variables

72x^2-180x+72=0

a = 72; b = -180; c = +72;
Δ = b2-4ac
Δ = -1802-4·72·72
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-108}{2*72}=\frac{72}{144}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+108}{2*72}=\frac{288}{144}
=2
$