(x+7)(3x-2)=(x+7)(x-6)

Solution for (x+7)(3x-2)=(x+7)(x-6) equation:

(x+7)(3x-2)=(x+7)(x-6)

We move all terms to the left:

(x+7)(3x-2)-((x+7)(x-6))=0

We multiply parentheses ..

(+3x^2-2x+21x-14)-((x+7)(x-6))=0


We calculate terms in parentheses: -((x+7)(x-6)), so:

(x+7)(x-6)

We multiply parentheses ..

(+x^2-6x+7x-42)

We get rid of parentheses

x^2-6x+7x-42

We add all the numbers together, and all the variables

x^2+x-42

Back to the equation:

-(x^2+x-42)


We get rid of parentheses

3x^2-x^2-2x+21x-x-14+42=0

We add all the numbers together, and all the variables

2x^2+18x+28=0

a = 2; b = 18; c = +28;
Δ = b2-4ac
Δ = 182-4·2·28
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*2}=\frac{-28}{4}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*2}=\frac{-8}{4}
=-2
$