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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(-1x-6)-((-6)(x+3))=0

We multiply parentheses

-1x^2-6x-((-6)(x+3))=0

We multiply parentheses ..

-1x^2-6x-((-6x-18))=0


We calculate terms in parentheses: -((-6x-18)), so:

(-6x-18)

We get rid of parentheses

-6x-18

Back to the equation:

-(-6x-18)


We get rid of parentheses

-1x^2-6x+6x+18=0

We add all the numbers together, and all the variables

-1x^2+18=0

a = -1; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-1)·18
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-1}=\frac{0-6\sqrt{2}}{-2}
=-\frac{6\sqrt{2}}{-2}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-1}=\frac{0+6\sqrt{2}}{-2}
=\frac{6\sqrt{2}}{-2}
=\frac{3\sqrt{2}}{-1}
$