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

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

Simplifying
4(3 + -1x) + -1(x + 2) = 6 + 3(x + -4)
(3 * 4 + -1x * 4) + -1(x + 2) = 6 + 3(x + -4)
(12 + -4x) + -1(x + 2) = 6 + 3(x + -4)

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

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

Combine like terms: 12 + -2 = 10
10 + -4x + -1x = 6 + 3(x + -4)

Combine like terms: -4x + -1x = -5x
10 + -5x = 6 + 3(x + -4)

Reorder the terms:
10 + -5x = 6 + 3(-4 + x)
10 + -5x = 6 + (-4 * 3 + x * 3)
10 + -5x = 6 + (-12 + 3x)

Combine like terms: 6 + -12 = -6
10 + -5x = -6 + 3x

Solving
10 + -5x = -6 + 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.
10 + -5x + -3x = -6 + 3x + -3x

Combine like terms: -5x + -3x = -8x
10 + -8x = -6 + 3x + -3x

Combine like terms: 3x + -3x = 0
10 + -8x = -6 + 0
10 + -8x = -6

Add '-10' to each side of the equation.
10 + -10 + -8x = -6 + -10

Combine like terms: 10 + -10 = 0
0 + -8x = -6 + -10
-8x = -6 + -10

Combine like terms: -6 + -10 = -16
-8x = -16

Divide each side by '-8'.
x = 2

Simplifying
x = 2