3(x-7)-(9-2x)=2(12-x)-(x-10)

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Solution for 3(x-7)-(9-2x)=2(12-x)-(x-10) equation: 


Simplifying
3(x + -7) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10)

Reorder the terms:
3(-7 + x) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10)
(-7 * 3 + x * 3) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10)
(-21 + 3x) + -1(9 + -2x) = 2(12 + -1x) + -1(x + -10)
-21 + 3x + (9 * -1 + -2x * -1) = 2(12 + -1x) + -1(x + -10)
-21 + 3x + (-9 + 2x) = 2(12 + -1x) + -1(x + -10)

Reorder the terms:
-21 + -9 + 3x + 2x = 2(12 + -1x) + -1(x + -10)

Combine like terms: -21 + -9 = -30
-30 + 3x + 2x = 2(12 + -1x) + -1(x + -10)

Combine like terms: 3x + 2x = 5x
-30 + 5x = 2(12 + -1x) + -1(x + -10)
-30 + 5x = (12 * 2 + -1x * 2) + -1(x + -10)
-30 + 5x = (24 + -2x) + -1(x + -10)

Reorder the terms:
-30 + 5x = 24 + -2x + -1(-10 + x)
-30 + 5x = 24 + -2x + (-10 * -1 + x * -1)
-30 + 5x = 24 + -2x + (10 + -1x)

Reorder the terms:
-30 + 5x = 24 + 10 + -2x + -1x

Combine like terms: 24 + 10 = 34
-30 + 5x = 34 + -2x + -1x

Combine like terms: -2x + -1x = -3x
-30 + 5x = 34 + -3x

Solving
-30 + 5x = 34 + -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.
-30 + 5x + 3x = 34 + -3x + 3x

Combine like terms: 5x + 3x = 8x
-30 + 8x = 34 + -3x + 3x

Combine like terms: -3x + 3x = 0
-30 + 8x = 34 + 0
-30 + 8x = 34

Add '30' to each side of the equation.
-30 + 30 + 8x = 34 + 30

Combine like terms: -30 + 30 = 0
0 + 8x = 34 + 30
8x = 34 + 30

Combine like terms: 34 + 30 = 64
8x = 64

Divide each side by '8'.
x = 8

Simplifying
x = 8

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