y-6+3(2y+3)=-5(y+1)

Solution for y-6+3(2y+3)=-5(y+1) equation:

Simplifying
y + -6 + 3(2y + 3) = -5(y + 1)

Reorder the terms:
y + -6 + 3(3 + 2y) = -5(y + 1)
y + -6 + (3 * 3 + 2y * 3) = -5(y + 1)
y + -6 + (9 + 6y) = -5(y + 1)

Reorder the terms:
-6 + 9 + y + 6y = -5(y + 1)

Combine like terms: -6 + 9 = 3
3 + y + 6y = -5(y + 1)

Combine like terms: y + 6y = 7y
3 + 7y = -5(y + 1)

Reorder the terms:
3 + 7y = -5(1 + y)
3 + 7y = (1 * -5 + y * -5)
3 + 7y = (-5 + -5y)

Solving
3 + 7y = -5 + -5y

Solving for variable 'y'.

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

Add '5y' to each side of the equation.
3 + 7y + 5y = -5 + -5y + 5y

Combine like terms: 7y + 5y = 12y
3 + 12y = -5 + -5y + 5y

Combine like terms: -5y + 5y = 0
3 + 12y = -5 + 0
3 + 12y = -5

Add '-3' to each side of the equation.
3 + -3 + 12y = -5 + -3

Combine like terms: 3 + -3 = 0
0 + 12y = -5 + -3
12y = -5 + -3

Combine like terms: -5 + -3 = -8
12y = -8

Divide each side by '12'.
y = -0.6666666667

Simplifying
y = -0.6666666667