3y(y+1)=-(6y+4)+y

Solution for 3y(y+1)=-(6y+4)+y equation:

Simplifying
3y(y + 1) = -1(6y + 4) + y

Reorder the terms:
3y(1 + y) = -1(6y + 4) + y
(1 * 3y + y * 3y) = -1(6y + 4) + y
(3y + 3y2) = -1(6y + 4) + y

Reorder the terms:
3y + 3y2 = -1(4 + 6y) + y
3y + 3y2 = (4 * -1 + 6y * -1) + y
3y + 3y2 = (-4 + -6y) + y

Combine like terms: -6y + y = -5y
3y + 3y2 = -4 + -5y

Solving
3y + 3y2 = -4 + -5y

Solving for variable 'y'.

Reorder the terms:
4 + 3y + 5y + 3y2 = -4 + -5y + 4 + 5y

Combine like terms: 3y + 5y = 8y
4 + 8y + 3y2 = -4 + -5y + 4 + 5y

Reorder the terms:
4 + 8y + 3y2 = -4 + 4 + -5y + 5y

Combine like terms: -4 + 4 = 0
4 + 8y + 3y2 = 0 + -5y + 5y
4 + 8y + 3y2 = -5y + 5y

Combine like terms: -5y + 5y = 0
4 + 8y + 3y2 = 0

Factor a trinomial.
(2 + y)(2 + 3y) = 0

Subproblem 1
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

Move all terms containing y to the left, all other terms to the right.

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

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

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

Simplifying
y = -2
Subproblem 2
Set the factor '(2 + 3y)' equal to zero and attempt to solve:

Simplifying
2 + 3y = 0

Solving
2 + 3y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3y = 0 + -2
3y = 0 + -2

Combine like terms: 0 + -2 = -2
3y = -2

Divide each side by '3'.
y = -0.6666666667

Simplifying
y = -0.6666666667
Solution
y = {-2, -0.6666666667}