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

Solution for 3(6x-2)=3x(2x-1)+0 equation:

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(3x(2x-1)+0), so:

3x(2x-1)+0

We add all the numbers together, and all the variables

3x(2x-1)

We multiply parentheses

6x^2-3x

Back to the equation:

-(6x^2-3x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-6x^2+21x-6=0

a = -6; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·(-6)·(-6)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{33}}{2*-6}=\frac{-21-3\sqrt{33}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{33}}{2*-6}=\frac{-21+3\sqrt{33}}{-12}
$