6(2x-1)-2(x-5)-4(x-3)=3(x-2)-4x

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Solution for 6(2x-1)-2(x-5)-4(x-3)=3(x-2)-4x equation: 


Simplifying
6(2x + -1) + -2(x + -5) + -4(x + -3) = 3(x + -2) + -4x

Reorder the terms:
6(-1 + 2x) + -2(x + -5) + -4(x + -3) = 3(x + -2) + -4x
(-1 * 6 + 2x * 6) + -2(x + -5) + -4(x + -3) = 3(x + -2) + -4x
(-6 + 12x) + -2(x + -5) + -4(x + -3) = 3(x + -2) + -4x

Reorder the terms:
-6 + 12x + -2(-5 + x) + -4(x + -3) = 3(x + -2) + -4x
-6 + 12x + (-5 * -2 + x * -2) + -4(x + -3) = 3(x + -2) + -4x
-6 + 12x + (10 + -2x) + -4(x + -3) = 3(x + -2) + -4x

Reorder the terms:
-6 + 12x + 10 + -2x + -4(-3 + x) = 3(x + -2) + -4x
-6 + 12x + 10 + -2x + (-3 * -4 + x * -4) = 3(x + -2) + -4x
-6 + 12x + 10 + -2x + (12 + -4x) = 3(x + -2) + -4x

Reorder the terms:
-6 + 10 + 12 + 12x + -2x + -4x = 3(x + -2) + -4x

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

Combine like terms: 4 + 12 = 16
16 + 12x + -2x + -4x = 3(x + -2) + -4x

Combine like terms: 12x + -2x = 10x
16 + 10x + -4x = 3(x + -2) + -4x

Combine like terms: 10x + -4x = 6x
16 + 6x = 3(x + -2) + -4x

Reorder the terms:
16 + 6x = 3(-2 + x) + -4x
16 + 6x = (-2 * 3 + x * 3) + -4x
16 + 6x = (-6 + 3x) + -4x

Combine like terms: 3x + -4x = -1x
16 + 6x = -6 + -1x

Solving
16 + 6x = -6 + -1x

Solving for variable 'x'.

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

Add 'x' to each side of the equation.
16 + 6x + x = -6 + -1x + x

Combine like terms: 6x + x = 7x
16 + 7x = -6 + -1x + x

Combine like terms: -1x + x = 0
16 + 7x = -6 + 0
16 + 7x = -6

Add '-16' to each side of the equation.
16 + -16 + 7x = -6 + -16

Combine like terms: 16 + -16 = 0
0 + 7x = -6 + -16
7x = -6 + -16

Combine like terms: -6 + -16 = -22
7x = -22

Divide each side by '7'.
x = -3.142857143

Simplifying
x = -3.142857143

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