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

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

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

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

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

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

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

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

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

Reorder the terms:
-2 + 1x = -6 + -3x + 2(-6 + 4x)
-2 + 1x = -6 + -3x + (-6 * 2 + 4x * 2)
-2 + 1x = -6 + -3x + (-12 + 8x)

Reorder the terms:
-2 + 1x = -6 + -12 + -3x + 8x

Combine like terms: -6 + -12 = -18
-2 + 1x = -18 + -3x + 8x

Combine like terms: -3x + 8x = 5x
-2 + 1x = -18 + 5x

Solving
-2 + 1x = -18 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
-2 + 1x + -5x = -18 + 5x + -5x

Combine like terms: 1x + -5x = -4x
-2 + -4x = -18 + 5x + -5x

Combine like terms: 5x + -5x = 0
-2 + -4x = -18 + 0
-2 + -4x = -18

Add '2' to each side of the equation.
-2 + 2 + -4x = -18 + 2

Combine like terms: -2 + 2 = 0
0 + -4x = -18 + 2
-4x = -18 + 2

Combine like terms: -18 + 2 = -16
-4x = -16

Divide each side by '-4'.
x = 4

Simplifying
x = 4