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) = (x + -3)

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

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

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

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

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

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

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

Solving
2 = -3 + x

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 + x + -1x

Combine like terms: x + -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 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5