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

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

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

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

Reorder the terms:
2 + 2Y + 6y = 3(Y + -1) + -2

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

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

Combine like terms: -3 + -2 = -5
2 + 2Y + 6y = -5 + 3Y

Solving
2 + 2Y + 6y = -5 + 3Y

Solving for variable 'Y'.

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

Add '-3Y' to each side of the equation.
2 + 2Y + -3Y + 6y = -5 + 3Y + -3Y

Combine like terms: 2Y + -3Y = -1Y
2 + -1Y + 6y = -5 + 3Y + -3Y

Combine like terms: 3Y + -3Y = 0
2 + -1Y + 6y = -5 + 0
2 + -1Y + 6y = -5

Add '-2' to each side of the equation.
2 + -1Y + -2 + 6y = -5 + -2

Reorder the terms:
2 + -2 + -1Y + 6y = -5 + -2

Combine like terms: 2 + -2 = 0
0 + -1Y + 6y = -5 + -2
-1Y + 6y = -5 + -2

Combine like terms: -5 + -2 = -7
-1Y + 6y = -7

Add '-6y' to each side of the equation.
-1Y + 6y + -6y = -7 + -6y

Combine like terms: 6y + -6y = 0
-1Y + 0 = -7 + -6y
-1Y = -7 + -6y

Divide each side by '-1'.
Y = 7 + 6y

Simplifying
Y = 7 + 6y