-27=-3(x-1)(x-3)

Solution for -27=-3(x-1)(x-3) equation:

-27=-3(x-1)(x-3)

We move all terms to the left:

-27-(-3(x-1)(x-3))=0

We multiply parentheses ..

-(-3(+x^2-3x-1x+3))-27=0


We calculate terms in parentheses: -(-3(+x^2-3x-1x+3)), so:

-3(+x^2-3x-1x+3)

We multiply parentheses

-3x^2+9x+3x-9

We add all the numbers together, and all the variables

-3x^2+12x-9

Back to the equation:

-(-3x^2+12x-9)


We get rid of parentheses

3x^2-12x+9-27=0

We add all the numbers together, and all the variables

3x^2-12x-18=0

a = 3; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·3·(-18)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{10}}{2*3}=\frac{12-6\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{10}}{2*3}=\frac{12+6\sqrt{10}}{6}
$