2y+15(-4+2y)=6y(-4+2y)

Solution for 2y+15(-4+2y)=6y(-4+2y) equation:

2y+15(-4+2y)=6y(-4+2y)

We move all terms to the left:

2y+15(-4+2y)-(6y(-4+2y))=0

We add all the numbers together, and all the variables

2y+15(2y-4)-(6y(2y-4))=0

We multiply parentheses

2y+30y-(6y(2y-4))-60=0


We calculate terms in parentheses: -(6y(2y-4)), so:

6y(2y-4)

We multiply parentheses

12y^2-24y

Back to the equation:

-(12y^2-24y)


We add all the numbers together, and all the variables

32y-(12y^2-24y)-60=0

We get rid of parentheses

-12y^2+32y+24y-60=0

We add all the numbers together, and all the variables

-12y^2+56y-60=0

a = -12; b = 56; c = -60;
Δ = b2-4ac
Δ = 562-4·(-12)·(-60)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-16}{2*-12}=\frac{-72}{-24}
=+3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+16}{2*-12}=\frac{-40}{-24}
=1+2/3
$