2(x-1)-3(x-2)+4(x-3)=13

Solution for 2(x-1)-3(x-2)+4(x-3)=13 equation:

Simplifying
2(x + -1) + -3(x + -2) + 4(x + -3) = 13

Reorder the terms:
2(-1 + x) + -3(x + -2) + 4(x + -3) = 13
(-1 * 2 + x * 2) + -3(x + -2) + 4(x + -3) = 13
(-2 + 2x) + -3(x + -2) + 4(x + -3) = 13

Reorder the terms:
-2 + 2x + -3(-2 + x) + 4(x + -3) = 13
-2 + 2x + (-2 * -3 + x * -3) + 4(x + -3) = 13
-2 + 2x + (6 + -3x) + 4(x + -3) = 13

Reorder the terms:
-2 + 2x + 6 + -3x + 4(-3 + x) = 13
-2 + 2x + 6 + -3x + (-3 * 4 + x * 4) = 13
-2 + 2x + 6 + -3x + (-12 + 4x) = 13

Reorder the terms:
-2 + 6 + -12 + 2x + -3x + 4x = 13

Combine like terms: -2 + 6 = 4
4 + -12 + 2x + -3x + 4x = 13

Combine like terms: 4 + -12 = -8
-8 + 2x + -3x + 4x = 13

Combine like terms: 2x + -3x = -1x
-8 + -1x + 4x = 13

Combine like terms: -1x + 4x = 3x
-8 + 3x = 13

Solving
-8 + 3x = 13

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + 3x = 13 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 13 + 8
3x = 13 + 8

Combine like terms: 13 + 8 = 21
3x = 21

Divide each side by '3'.
x = 7

Simplifying
x = 7