3(x-2)-2(x-3)=4(x-5)+5(x-8)

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Solution for 3(x-2)-2(x-3)=4(x-5)+5(x-8) equation:


Simplifying
3(x + -2) + -2(x + -3) = 4(x + -5) + 5(x + -8)

Reorder the terms:
3(-2 + x) + -2(x + -3) = 4(x + -5) + 5(x + -8)
(-2 * 3 + x * 3) + -2(x + -3) = 4(x + -5) + 5(x + -8)
(-6 + 3x) + -2(x + -3) = 4(x + -5) + 5(x + -8)

Reorder the terms:
-6 + 3x + -2(-3 + x) = 4(x + -5) + 5(x + -8)
-6 + 3x + (-3 * -2 + x * -2) = 4(x + -5) + 5(x + -8)
-6 + 3x + (6 + -2x) = 4(x + -5) + 5(x + -8)

Reorder the terms:
-6 + 6 + 3x + -2x = 4(x + -5) + 5(x + -8)

Combine like terms: -6 + 6 = 0
0 + 3x + -2x = 4(x + -5) + 5(x + -8)
3x + -2x = 4(x + -5) + 5(x + -8)

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

Reorder the terms:
1x = 4(-5 + x) + 5(x + -8)
1x = (-5 * 4 + x * 4) + 5(x + -8)
1x = (-20 + 4x) + 5(x + -8)

Reorder the terms:
1x = -20 + 4x + 5(-8 + x)
1x = -20 + 4x + (-8 * 5 + x * 5)
1x = -20 + 4x + (-40 + 5x)

Reorder the terms:
1x = -20 + -40 + 4x + 5x

Combine like terms: -20 + -40 = -60
1x = -60 + 4x + 5x

Combine like terms: 4x + 5x = 9x
1x = -60 + 9x

Solving
1x = -60 + 9x

Solving for variable 'x'.

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

Add '-9x' to each side of the equation.
1x + -9x = -60 + 9x + -9x

Combine like terms: 1x + -9x = -8x
-8x = -60 + 9x + -9x

Combine like terms: 9x + -9x = 0
-8x = -60 + 0
-8x = -60

Divide each side by '-8'.
x = 7.5

Simplifying
x = 7.5

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