y+(y-4)=(y+2)-(y-8)

Solution for y+(y-4)=(y+2)-(y-8) equation:

Simplifying
y + (y + -4) = (y + 2) + -1(y + -8)

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

Remove parenthesis around (-4 + y)
y + -4 + y = (y + 2) + -1(y + -8)

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

Combine like terms: y + y = 2y
-4 + 2y = (y + 2) + -1(y + -8)

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

Remove parenthesis around (2 + y)
-4 + 2y = 2 + y + -1(y + -8)

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

Reorder the terms:
-4 + 2y = 2 + 8 + y + -1y

Combine like terms: 2 + 8 = 10
-4 + 2y = 10 + y + -1y

Combine like terms: y + -1y = 0
-4 + 2y = 10 + 0
-4 + 2y = 10

Solving
-4 + 2y = 10

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + 2y = 10 + 4

Combine like terms: -4 + 4 = 0
0 + 2y = 10 + 4
2y = 10 + 4

Combine like terms: 10 + 4 = 14
2y = 14

Divide each side by '2'.
y = 7

Simplifying
y = 7