-(x-7)+4(7-x)=6(x-2)-3(3-x)

Solution for -(x-7)+4(7-x)=6(x-2)-3(3-x) equation:

Simplifying
-1(x + -7) + 4(7 + -1x) = 6(x + -2) + -3(3 + -1x)

Reorder the terms:
-1(-7 + x) + 4(7 + -1x) = 6(x + -2) + -3(3 + -1x)
(-7 * -1 + x * -1) + 4(7 + -1x) = 6(x + -2) + -3(3 + -1x)
(7 + -1x) + 4(7 + -1x) = 6(x + -2) + -3(3 + -1x)
7 + -1x + (7 * 4 + -1x * 4) = 6(x + -2) + -3(3 + -1x)
7 + -1x + (28 + -4x) = 6(x + -2) + -3(3 + -1x)

Reorder the terms:
7 + 28 + -1x + -4x = 6(x + -2) + -3(3 + -1x)

Combine like terms: 7 + 28 = 35
35 + -1x + -4x = 6(x + -2) + -3(3 + -1x)

Combine like terms: -1x + -4x = -5x
35 + -5x = 6(x + -2) + -3(3 + -1x)

Reorder the terms:
35 + -5x = 6(-2 + x) + -3(3 + -1x)
35 + -5x = (-2 * 6 + x * 6) + -3(3 + -1x)
35 + -5x = (-12 + 6x) + -3(3 + -1x)
35 + -5x = -12 + 6x + (3 * -3 + -1x * -3)
35 + -5x = -12 + 6x + (-9 + 3x)

Reorder the terms:
35 + -5x = -12 + -9 + 6x + 3x

Combine like terms: -12 + -9 = -21
35 + -5x = -21 + 6x + 3x

Combine like terms: 6x + 3x = 9x
35 + -5x = -21 + 9x

Solving
35 + -5x = -21 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
35 + -5x + -9x = -21 + 9x + -9x

Combine like terms: -5x + -9x = -14x
35 + -14x = -21 + 9x + -9x

Combine like terms: 9x + -9x = 0
35 + -14x = -21 + 0
35 + -14x = -21

Add '-35' to each side of the equation.
35 + -35 + -14x = -21 + -35

Combine like terms: 35 + -35 = 0
0 + -14x = -21 + -35
-14x = -21 + -35

Combine like terms: -21 + -35 = -56
-14x = -56

Divide each side by '-14'.
x = 4

Simplifying
x = 4