x=(x-3)(x+6)

Solution for x=(x-3)(x+6) equation:

x=(x-3)(x+6)

We move all terms to the left:

x-((x-3)(x+6))=0

We multiply parentheses ..

-((+x^2+6x-3x-18))+x=0


We calculate terms in parentheses: -((+x^2+6x-3x-18)), so:

(+x^2+6x-3x-18)

We get rid of parentheses

x^2+6x-3x-18

We add all the numbers together, and all the variables

x^2+3x-18

Back to the equation:

-(x^2+3x-18)


We add all the numbers together, and all the variables

x-(x^2+3x-18)=0

We get rid of parentheses

-x^2+x-3x+18=0

We add all the numbers together, and all the variables

-1x^2-2x+18=0

a = -1; b = -2; c = +18;
Δ = b2-4ac
Δ = -22-4·(-1)·18
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-1}=\frac{2-2\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-1}=\frac{2+2\sqrt{19}}{-2}
$