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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(x+3)(x+3)

We multiply parentheses ..

(+x^2+3x+3x+9)

We get rid of parentheses

x^2+3x+3x+9

We add all the numbers together, and all the variables

x^2+6x+9

Back to the equation:

-(x^2+6x+9)


We get rid of parentheses

2x^2-x^2+2x+3x-6x+3-9=0

We add all the numbers together, and all the variables

x^2-1x-6=0

a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
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{-(-1)-5}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2}
=3
$