(x(x-4))/((x-2)(x+6))=0

Solution for (x(x-4))/((x-2)(x+6))=0 equation:

(x(x-4))/((x-2)(x+6))=0


Domain of the equation: ((x-2)(x+6))!=0

x∈R


We multiply parentheses ..

(x(x-4))/((+x^2+6x-2x-12))=0

We multiply all the terms by the denominator


(x(x-4))=0


We calculate terms in parentheses: +(x(x-4)), so:

x(x-4)

We multiply parentheses

x^2-4x

Back to the equation:

+(x^2-4x)


We get rid of parentheses

x^2-4x=0

a = 1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·1·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*1}=\frac{8}{2}
=4
$