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

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

Simplifying
3y(y + 1) = 2(y + -3)

Reorder the terms:
3y(1 + y) = 2(y + -3)
(1 * 3y + y * 3y) = 2(y + -3)
(3y + 3y2) = 2(y + -3)

Reorder the terms:
3y + 3y2 = 2(-3 + y)
3y + 3y2 = (-3 * 2 + y * 2)
3y + 3y2 = (-6 + 2y)

Solving
3y + 3y2 = -6 + 2y

Solving for variable 'y'.

Reorder the terms:
6 + 3y + -2y + 3y2 = -6 + 2y + 6 + -2y

Combine like terms: 3y + -2y = 1y
6 + 1y + 3y2 = -6 + 2y + 6 + -2y

Reorder the terms:
6 + 1y + 3y2 = -6 + 6 + 2y + -2y

Combine like terms: -6 + 6 = 0
6 + 1y + 3y2 = 0 + 2y + -2y
6 + 1y + 3y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
6 + 1y + 3y2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 0.3333333333y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + 0.3333333333y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 0.3333333333y + y2 = 0 + -2
0.3333333333y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
0.3333333333y + y2 = -2

The y term is 0.3333333333y.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333y + 0.02777777779 + y2 = -2 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333y + y2 = -2 + 0.02777777779

Combine like terms: -2 + 0.02777777779 = -1.97222222221
0.02777777779 + 0.3333333333y + y2 = -1.97222222221

Factor a perfect square on the left side:
(y + 0.1666666667)(y + 0.1666666667) = -1.97222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.