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

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

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

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

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

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

Combine like terms: -2 + 4 = 2
2 + 2x + -2x = -1(-1x + -3)

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

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

Solving
2 = 3 + 1x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
2 + -1x = 3 + 1x + -1x

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 3 + -2

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

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

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

Simplifying
x = -1