2c-3(c+1)=c(c+3)

Solution for 2c-3(c+1)=c(c+3) equation:

2c-3(c+1)=c(c+3)

We move all terms to the left:

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

We multiply parentheses

2c-3c-(c(c+3))-3=0


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

c(c+3)

We multiply parentheses

c^2+3c

Back to the equation:

-(c^2+3c)


We add all the numbers together, and all the variables

-1c-(c^2+3c)-3=0

We get rid of parentheses

-c^2-1c-3c-3=0

We add all the numbers together, and all the variables

-1c^2-4c-3=0

a = -1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·(-1)·(-3)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*-1}=\frac{2}{-2}
=-1
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*-1}=\frac{6}{-2}
=-3
$