(6-x)(3-x)=(2)(6-2x)

Solution for (6-x)(3-x)=(2)(6-2x) equation:

(6-x)(3-x)=(2)(6-2x)

We move all terms to the left:

(6-x)(3-x)-((2)(6-2x))=0

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


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

2(-2x+6)

We multiply parentheses

-4x+12

Back to the equation:

-(-4x+12)


We get rid of parentheses

x^2-3x-6x+4x+18-12=0

We add all the numbers together, and all the variables

x^2-5x+6=0

a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2}
=3
$