Y-[2(1-2y)-3(2-y)]=2(y+2)

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

Simplifying
Y + -1[2(1 + -2y) + -3(2 + -1y)] = 2(y + 2)
Y + -1[(1 * 2 + -2y * 2) + -3(2 + -1y)] = 2(y + 2)
Y + -1[(2 + -4y) + -3(2 + -1y)] = 2(y + 2)
Y + -1[2 + -4y + (2 * -3 + -1y * -3)] = 2(y + 2)
Y + -1[2 + -4y + (-6 + 3y)] = 2(y + 2)

Reorder the terms:
Y + -1[2 + -6 + -4y + 3y] = 2(y + 2)

Combine like terms: 2 + -6 = -4
Y + -1[-4 + -4y + 3y] = 2(y + 2)

Combine like terms: -4y + 3y = -1y
Y + -1[-4 + -1y] = 2(y + 2)
Y + [-4 * -1 + -1y * -1] = 2(y + 2)
Y + [4 + 1y] = 2(y + 2)

Reorder the terms:
4 + Y + 1y = 2(y + 2)

Reorder the terms:
4 + Y + 1y = 2(2 + y)
4 + Y + 1y = (2 * 2 + y * 2)
4 + Y + 1y = (4 + 2y)

Add '-4' to each side of the equation.
4 + Y + -4 + 1y = 4 + -4 + 2y

Reorder the terms:
4 + -4 + Y + 1y = 4 + -4 + 2y

Combine like terms: 4 + -4 = 0
0 + Y + 1y = 4 + -4 + 2y
Y + 1y = 4 + -4 + 2y

Combine like terms: 4 + -4 = 0
Y + 1y = 0 + 2y
Y + 1y = 2y

Solving
Y + 1y = 2y

Solving for variable 'Y'.

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

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

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

Combine like terms: 2y + -1y = 1y
Y = 1y

Simplifying
Y = 1y