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4\left(2x+3\right)-3\left(3x-2\right)=12
Multiply both sides of the equation by 12, the least common multiple of 3,4.
8x+12-3\left(3x-2\right)=12
Use the distributive property to multiply 4 by 2x+3.
8x+12-9x+6=12
Use the distributive property to multiply -3 by 3x-2.
-x+12+6=12
Combine 8x and -9x to get -x.
-x+18=12
Add 12 and 6 to get 18.
-x=12-18
Subtract 18 from both sides.
-x=-6
Subtract 18 from 12 to get -6.
x=6
Multiply both sides by -1.