1-(1-x)+2(x-3)=4-(6-x)

Solution for 1-(1-x)+2(x-3)=4-(6-x) equation:

Simplifying
1 + -1(1 + -1x) + 2(x + -3) = 4 + -1(6 + -1x)
1 + (1 * -1 + -1x * -1) + 2(x + -3) = 4 + -1(6 + -1x)
1 + (-1 + 1x) + 2(x + -3) = 4 + -1(6 + -1x)

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

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

Combine like terms: 1 + -1 = 0
0 + -6 + 1x + 2x = 4 + -1(6 + -1x)
-6 + 1x + 2x = 4 + -1(6 + -1x)

Combine like terms: 1x + 2x = 3x
-6 + 3x = 4 + -1(6 + -1x)
-6 + 3x = 4 + (6 * -1 + -1x * -1)
-6 + 3x = 4 + (-6 + 1x)

Combine like terms: 4 + -6 = -2
-6 + 3x = -2 + 1x

Solving
-6 + 3x = -2 + 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.
-6 + 3x + -1x = -2 + 1x + -1x

Combine like terms: 3x + -1x = 2x
-6 + 2x = -2 + 1x + -1x

Combine like terms: 1x + -1x = 0
-6 + 2x = -2 + 0
-6 + 2x = -2

Add '6' to each side of the equation.
-6 + 6 + 2x = -2 + 6

Combine like terms: -6 + 6 = 0
0 + 2x = -2 + 6
2x = -2 + 6

Combine like terms: -2 + 6 = 4
2x = 4

Divide each side by '2'.
x = 2

Simplifying
x = 2