2(y+3)-4(2y+1)=y-3(2+y)

Solution for 2(y+3)-4(2y+1)=y-3(2+y) equation:

Simplifying
2(y + 3) + -4(2y + 1) = y + -3(2 + y)

Reorder the terms:
2(3 + y) + -4(2y + 1) = y + -3(2 + y)
(3 * 2 + y * 2) + -4(2y + 1) = y + -3(2 + y)
(6 + 2y) + -4(2y + 1) = y + -3(2 + y)

Reorder the terms:
6 + 2y + -4(1 + 2y) = y + -3(2 + y)
6 + 2y + (1 * -4 + 2y * -4) = y + -3(2 + y)
6 + 2y + (-4 + -8y) = y + -3(2 + y)

Reorder the terms:
6 + -4 + 2y + -8y = y + -3(2 + y)

Combine like terms: 6 + -4 = 2
2 + 2y + -8y = y + -3(2 + y)

Combine like terms: 2y + -8y = -6y
2 + -6y = y + -3(2 + y)
2 + -6y = y + (2 * -3 + y * -3)
2 + -6y = y + (-6 + -3y)

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

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

Solving
2 + -6y = -6 + -2y

Solving for variable 'y'.

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

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

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

Combine like terms: -2y + 2y = 0
2 + -4y = -6 + 0
2 + -4y = -6

Add '-2' to each side of the equation.
2 + -2 + -4y = -6 + -2

Combine like terms: 2 + -2 = 0
0 + -4y = -6 + -2
-4y = -6 + -2

Combine like terms: -6 + -2 = -8
-4y = -8

Divide each side by '-4'.
y = 2

Simplifying
y = 2