-5(-3y+3)-3y=y(y-2)-3

Solution for -5(-3y+3)-3y=y(y-2)-3 equation:

-5(-3y+3)-3y=y(y-2)-3

We move all terms to the left:

-5(-3y+3)-3y-(y(y-2)-3)=0

We add all the numbers together, and all the variables

-3y-5(-3y+3)-(y(y-2)-3)=0

We multiply parentheses

-3y+15y-(y(y-2)-3)-15=0


We calculate terms in parentheses: -(y(y-2)-3), so:

y(y-2)-3

We multiply parentheses

y^2-2y-3

Back to the equation:

-(y^2-2y-3)


We add all the numbers together, and all the variables

12y-(y^2-2y-3)-15=0

We get rid of parentheses

-y^2+12y+2y+3-15=0

We add all the numbers together, and all the variables

-1y^2+14y-12=0

a = -1; b = 14; c = -12;
Δ = b2-4ac
Δ = 142-4·(-1)·(-12)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{37}}{2*-1}=\frac{-14-2\sqrt{37}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{37}}{2*-1}=\frac{-14+2\sqrt{37}}{-2}
$