3(x+13)-2(x+2)=2(x-2)+3(x-3)

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Solution for 3(x+13)-2(x+2)=2(x-2)+3(x-3) equation: 


Simplifying
3(x + 13) + -2(x + 2) = 2(x + -2) + 3(x + -3)

Reorder the terms:
3(13 + x) + -2(x + 2) = 2(x + -2) + 3(x + -3)
(13 * 3 + x * 3) + -2(x + 2) = 2(x + -2) + 3(x + -3)
(39 + 3x) + -2(x + 2) = 2(x + -2) + 3(x + -3)

Reorder the terms:
39 + 3x + -2(2 + x) = 2(x + -2) + 3(x + -3)
39 + 3x + (2 * -2 + x * -2) = 2(x + -2) + 3(x + -3)
39 + 3x + (-4 + -2x) = 2(x + -2) + 3(x + -3)

Reorder the terms:
39 + -4 + 3x + -2x = 2(x + -2) + 3(x + -3)

Combine like terms: 39 + -4 = 35
35 + 3x + -2x = 2(x + -2) + 3(x + -3)

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

Reorder the terms:
35 + 1x = 2(-2 + x) + 3(x + -3)
35 + 1x = (-2 * 2 + x * 2) + 3(x + -3)
35 + 1x = (-4 + 2x) + 3(x + -3)

Reorder the terms:
35 + 1x = -4 + 2x + 3(-3 + x)
35 + 1x = -4 + 2x + (-3 * 3 + x * 3)
35 + 1x = -4 + 2x + (-9 + 3x)

Reorder the terms:
35 + 1x = -4 + -9 + 2x + 3x

Combine like terms: -4 + -9 = -13
35 + 1x = -13 + 2x + 3x

Combine like terms: 2x + 3x = 5x
35 + 1x = -13 + 5x

Solving
35 + 1x = -13 + 5x

Solving for variable 'x'.

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

Add '-5x' to each side of the equation.
35 + 1x + -5x = -13 + 5x + -5x

Combine like terms: 1x + -5x = -4x
35 + -4x = -13 + 5x + -5x

Combine like terms: 5x + -5x = 0
35 + -4x = -13 + 0
35 + -4x = -13

Add '-35' to each side of the equation.
35 + -35 + -4x = -13 + -35

Combine like terms: 35 + -35 = 0
0 + -4x = -13 + -35
-4x = -13 + -35

Combine like terms: -13 + -35 = -48
-4x = -48

Divide each side by '-4'.
x = 12

Simplifying
x = 12

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