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

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

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

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

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

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

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

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

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

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

Reorder the terms:
-1x = 1 + 3 + x + -1x

Combine like terms: 1 + 3 = 4
-1x = 4 + x + -1x

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

Solving
-1x = 4

Solving for variable 'x'.

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4