(3x+1)(1-6x)-(3x+7)(3x+1)=0

Solution for (3x+1)(1-6x)-(3x+7)(3x+1)=0 equation:

(3x+1)(1-6x)-(3x+7)(3x+1)=0

We add all the numbers together, and all the variables

(3x+1)(-6x+1)-(3x+7)(3x+1)=0

We multiply parentheses ..

(-18x^2+3x-6x+1)-(3x+7)(3x+1)=0

We get rid of parentheses

-18x^2+3x-6x-(3x+7)(3x+1)+1=0

We multiply parentheses ..

-18x^2-(+9x^2+3x+21x+7)+3x-6x+1=0

We add all the numbers together, and all the variables

-18x^2-(+9x^2+3x+21x+7)-3x+1=0

We get rid of parentheses

-18x^2-9x^2-3x-21x-3x-7+1=0

We add all the numbers together, and all the variables

-27x^2-27x-6=0

a = -27; b = -27; c = -6;
Δ = b2-4ac
Δ = -272-4·(-27)·(-6)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-9}{2*-27}=\frac{18}{-54}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+9}{2*-27}=\frac{36}{-54}
=-2/3
$