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3\left(x-1\right)-2\left(x+3\right)=6
Multiply both sides of the equation by 6, the least common multiple of 2,3.
3x-3-2\left(x+3\right)=6
Use the distributive property to multiply 3 by x-1.
3x-3-2x-6=6
Use the distributive property to multiply -2 by x+3.
x-3-6=6
Combine 3x and -2x to get x.
x-9=6
Subtract 6 from -3 to get -9.
x=6+9
Add 9 to both sides.
x=15
Add 6 and 9 to get 15.