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4\left(2x+1\right)-3\left(x-3\right)=6x
Multiply both sides of the equation by 12, the least common multiple of 3,4,2.
8x+4-3\left(x-3\right)=6x
Use the distributive property to multiply 4 by 2x+1.
8x+4-3x+9=6x
Use the distributive property to multiply -3 by x-3.
5x+4+9=6x
Combine 8x and -3x to get 5x.
5x+13=6x
Add 4 and 9 to get 13.
5x+13-6x=0
Subtract 6x from both sides.
-x+13=0
Combine 5x and -6x to get -x.
-x=-13
Subtract 13 from both sides. Anything subtracted from zero gives its negation.
x=13
Multiply both sides by -1.