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

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

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

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

Remove parenthesis around (2 + y)
2 + y + -2(y + 3) = 4(x + 1)

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

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

Combine like terms: 2 + -6 = -4
-4 + y + -2y = 4(x + 1)

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

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

Solving
-4 + -1y = 4 + 4x

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 + -1y = 4 + 4 + 4x

Combine like terms: -4 + 4 = 0
0 + -1y = 4 + 4 + 4x
-1y = 4 + 4 + 4x

Combine like terms: 4 + 4 = 8
-1y = 8 + 4x

Divide each side by '-1'.
y = -8 + -4x

Simplifying
y = -8 + -4x