(x-6)(2x+1)=(x-6)(x-4)

Solution for (x-6)(2x+1)=(x-6)(x-4) equation:

(x-6)(2x+1)=(x-6)(x-4)

We move all terms to the left:

(x-6)(2x+1)-((x-6)(x-4))=0

We multiply parentheses ..

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


We calculate terms in parentheses: -((x-6)(x-4)), so:

(x-6)(x-4)

We multiply parentheses ..

(+x^2-4x-6x+24)

We get rid of parentheses

x^2-4x-6x+24

We add all the numbers together, and all the variables

x^2-10x+24

Back to the equation:

-(x^2-10x+24)


We get rid of parentheses

2x^2-x^2+x-12x+10x-6-24=0

We add all the numbers together, and all the variables

x^2-1x-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*1}=\frac{-10}{2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$