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

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


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

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

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

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

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

Combine like terms: -2 + 6 = 4
4 + -12 + 2x + -3x + 4x = 2(x + 5)

Combine like terms: 4 + -12 = -8
-8 + 2x + -3x + 4x = 2(x + 5)

Combine like terms: 2x + -3x = -1x
-8 + -1x + 4x = 2(x + 5)

Combine like terms: -1x + 4x = 3x
-8 + 3x = 2(x + 5)

Reorder the terms:
-8 + 3x = 2(5 + x)
-8 + 3x = (5 * 2 + x * 2)
-8 + 3x = (10 + 2x)

Solving
-8 + 3x = 10 + 2x

Solving for variable 'x'.

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

Add '-2x' to each side of the equation.
-8 + 3x + -2x = 10 + 2x + -2x

Combine like terms: 3x + -2x = 1x
-8 + 1x = 10 + 2x + -2x

Combine like terms: 2x + -2x = 0
-8 + 1x = 10 + 0
-8 + 1x = 10

Add '8' to each side of the equation.
-8 + 8 + 1x = 10 + 8

Combine like terms: -8 + 8 = 0
0 + 1x = 10 + 8
1x = 10 + 8

Combine like terms: 10 + 8 = 18
1x = 18

Divide each side by '1'.
x = 18

Simplifying
x = 18

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