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

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

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

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

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

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

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

Reorder the terms:
6 + -4x = -3 + x + -3x

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

Solving
6 + -4x = -3 + -2x

Solving for variable 'x'.

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

Add '2x' to each side of the equation.
6 + -4x + 2x = -3 + -2x + 2x

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

Combine like terms: -2x + 2x = 0
6 + -2x = -3 + 0
6 + -2x = -3

Add '-6' to each side of the equation.
6 + -6 + -2x = -3 + -6

Combine like terms: 6 + -6 = 0
0 + -2x = -3 + -6
-2x = -3 + -6

Combine like terms: -3 + -6 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5