y(y+1)=-3y-6

Solution for y(y+1)=-3y-6 equation:

Simplifying
y(y + 1) = -3y + -6

Reorder the terms:
y(1 + y) = -3y + -6
(1 * y + y * y) = -3y + -6
(1y + y2) = -3y + -6

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

Solving
1y + y2 = -6 + -3y

Solving for variable 'y'.

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

Combine like terms: 1y + 3y = 4y
6 + 4y + y2 = -6 + -3y + 6 + 3y

Reorder the terms:
6 + 4y + y2 = -6 + 6 + -3y + 3y

Combine like terms: -6 + 6 = 0
6 + 4y + y2 = 0 + -3y + 3y
6 + 4y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
6 + 4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 4y + -6 + y2 = 0 + -6

Reorder the terms:
6 + -6 + 4y + y2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 4y + y2 = 0 + -6
4y + y2 = 0 + -6

Combine like terms: 0 + -6 = -6
4y + y2 = -6

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = -6 + 4

Reorder the terms:
4 + 4y + y2 = -6 + 4

Combine like terms: -6 + 4 = -2
4 + 4y + y2 = -2

Factor a perfect square on the left side:
(y + 2)(y + 2) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.