(3x+1)(2x+2)=x(3x+1)

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

(3x+1)(2x+2)=x(3x+1)

We move all terms to the left:

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

We multiply parentheses ..

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


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

x(3x+1)

We multiply parentheses

3x^2+x

Back to the equation:

-(3x^2+x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+7x+2=0

a = 3; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·3·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*3}=\frac{-12}{6}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*3}=\frac{-2}{6}
=-1/3
$