(w-1)-2w+1-(w-2)=(3-w)+(-3+w)

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

Simplifying
(w + -1) + -2w + 1 + -1(w + -2) = (3 + -1w) + (-3 + w)

Reorder the terms:
(-1 + w) + -2w + 1 + -1(w + -2) = (3 + -1w) + (-3 + w)

Remove parenthesis around (-1 + w)
-1 + w + -2w + 1 + -1(w + -2) = (3 + -1w) + (-3 + w)

Reorder the terms:
-1 + w + -2w + 1 + -1(-2 + w) = (3 + -1w) + (-3 + w)
-1 + w + -2w + 1 + (-2 * -1 + w * -1) = (3 + -1w) + (-3 + w)
-1 + w + -2w + 1 + (2 + -1w) = (3 + -1w) + (-3 + w)

Reorder the terms:
-1 + 1 + 2 + w + -2w + -1w = (3 + -1w) + (-3 + w)

Combine like terms: -1 + 1 = 0
0 + 2 + w + -2w + -1w = (3 + -1w) + (-3 + w)
2 + w + -2w + -1w = (3 + -1w) + (-3 + w)

Combine like terms: w + -2w = -1w
2 + -1w + -1w = (3 + -1w) + (-3 + w)

Combine like terms: -1w + -1w = -2w
2 + -2w = (3 + -1w) + (-3 + w)

Remove parenthesis around (3 + -1w)
2 + -2w = 3 + -1w + (-3 + w)

Remove parenthesis around (-3 + w)
2 + -2w = 3 + -1w + -3 + w

Reorder the terms:
2 + -2w = 3 + -3 + -1w + w

Combine like terms: 3 + -3 = 0
2 + -2w = 0 + -1w + w
2 + -2w = -1w + w

Combine like terms: -1w + w = 0
2 + -2w = 0

Solving
2 + -2w = 0

Solving for variable 'w'.

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

Add '-2' to each side of the equation.
2 + -2 + -2w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -2w = 0 + -2
-2w = 0 + -2

Combine like terms: 0 + -2 = -2
-2w = -2

Divide each side by '-2'.
w = 1

Simplifying
w = 1