3(x-5)-2(x-4)=3(x-3)-6(x-2)

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Solution for 3(x-5)-2(x-4)=3(x-3)-6(x-2) equation: 


Simplifying
3(x + -5) + -2(x + -4) = 3(x + -3) + -6(x + -2)

Reorder the terms:
3(-5 + x) + -2(x + -4) = 3(x + -3) + -6(x + -2)
(-5 * 3 + x * 3) + -2(x + -4) = 3(x + -3) + -6(x + -2)
(-15 + 3x) + -2(x + -4) = 3(x + -3) + -6(x + -2)

Reorder the terms:
-15 + 3x + -2(-4 + x) = 3(x + -3) + -6(x + -2)
-15 + 3x + (-4 * -2 + x * -2) = 3(x + -3) + -6(x + -2)
-15 + 3x + (8 + -2x) = 3(x + -3) + -6(x + -2)

Reorder the terms:
-15 + 8 + 3x + -2x = 3(x + -3) + -6(x + -2)

Combine like terms: -15 + 8 = -7
-7 + 3x + -2x = 3(x + -3) + -6(x + -2)

Combine like terms: 3x + -2x = 1x
-7 + 1x = 3(x + -3) + -6(x + -2)

Reorder the terms:
-7 + 1x = 3(-3 + x) + -6(x + -2)
-7 + 1x = (-3 * 3 + x * 3) + -6(x + -2)
-7 + 1x = (-9 + 3x) + -6(x + -2)

Reorder the terms:
-7 + 1x = -9 + 3x + -6(-2 + x)
-7 + 1x = -9 + 3x + (-2 * -6 + x * -6)
-7 + 1x = -9 + 3x + (12 + -6x)

Reorder the terms:
-7 + 1x = -9 + 12 + 3x + -6x

Combine like terms: -9 + 12 = 3
-7 + 1x = 3 + 3x + -6x

Combine like terms: 3x + -6x = -3x
-7 + 1x = 3 + -3x

Solving
-7 + 1x = 3 + -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.
-7 + 1x + 3x = 3 + -3x + 3x

Combine like terms: 1x + 3x = 4x
-7 + 4x = 3 + -3x + 3x

Combine like terms: -3x + 3x = 0
-7 + 4x = 3 + 0
-7 + 4x = 3

Add '7' to each side of the equation.
-7 + 7 + 4x = 3 + 7

Combine like terms: -7 + 7 = 0
0 + 4x = 3 + 7
4x = 3 + 7

Combine like terms: 3 + 7 = 10
4x = 10

Divide each side by '4'.
x = 2.5

Simplifying
x = 2.5

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