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

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

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

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

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

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

Combine like terms: 6 + 6 = 12
-3 + 2x = 12 + -3x

Solving
-3 + 2x = 12 + -3x

Solving for variable 'x'.

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

Add '3x' to each side of the equation.
-3 + 2x + 3x = 12 + -3x + 3x

Combine like terms: 2x + 3x = 5x
-3 + 5x = 12 + -3x + 3x

Combine like terms: -3x + 3x = 0
-3 + 5x = 12 + 0
-3 + 5x = 12

Add '3' to each side of the equation.
-3 + 3 + 5x = 12 + 3

Combine like terms: -3 + 3 = 0
0 + 5x = 12 + 3
5x = 12 + 3

Combine like terms: 12 + 3 = 15
5x = 15

Divide each side by '5'.
x = 3

Simplifying
x = 3