3(x+10)-2(x+4)=2(x-2)+3(x-2)

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Solution for 3(x+10)-2(x+4)=2(x-2)+3(x-2) equation: 


Simplifying
3(x + 10) + -2(x + 4) = 2(x + -2) + 3(x + -2)

Reorder the terms:
3(10 + x) + -2(x + 4) = 2(x + -2) + 3(x + -2)
(10 * 3 + x * 3) + -2(x + 4) = 2(x + -2) + 3(x + -2)
(30 + 3x) + -2(x + 4) = 2(x + -2) + 3(x + -2)

Reorder the terms:
30 + 3x + -2(4 + x) = 2(x + -2) + 3(x + -2)
30 + 3x + (4 * -2 + x * -2) = 2(x + -2) + 3(x + -2)
30 + 3x + (-8 + -2x) = 2(x + -2) + 3(x + -2)

Reorder the terms:
30 + -8 + 3x + -2x = 2(x + -2) + 3(x + -2)

Combine like terms: 30 + -8 = 22
22 + 3x + -2x = 2(x + -2) + 3(x + -2)

Combine like terms: 3x + -2x = 1x
22 + 1x = 2(x + -2) + 3(x + -2)

Reorder the terms:
22 + 1x = 2(-2 + x) + 3(x + -2)
22 + 1x = (-2 * 2 + x * 2) + 3(x + -2)
22 + 1x = (-4 + 2x) + 3(x + -2)

Reorder the terms:
22 + 1x = -4 + 2x + 3(-2 + x)
22 + 1x = -4 + 2x + (-2 * 3 + x * 3)
22 + 1x = -4 + 2x + (-6 + 3x)

Reorder the terms:
22 + 1x = -4 + -6 + 2x + 3x

Combine like terms: -4 + -6 = -10
22 + 1x = -10 + 2x + 3x

Combine like terms: 2x + 3x = 5x
22 + 1x = -10 + 5x

Solving
22 + 1x = -10 + 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.
22 + 1x + -5x = -10 + 5x + -5x

Combine like terms: 1x + -5x = -4x
22 + -4x = -10 + 5x + -5x

Combine like terms: 5x + -5x = 0
22 + -4x = -10 + 0
22 + -4x = -10

Add '-22' to each side of the equation.
22 + -22 + -4x = -10 + -22

Combine like terms: 22 + -22 = 0
0 + -4x = -10 + -22
-4x = -10 + -22

Combine like terms: -10 + -22 = -32
-4x = -32

Divide each side by '-4'.
x = 8

Simplifying
x = 8

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