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3\left(x+3\right)-2\left(x-3\right)=0
Multiply both sides of the equation by 18, the least common multiple of 6,9.
3x+9-2\left(x-3\right)=0
Use the distributive property to multiply 3 by x+3.
3x+9-2x+6=0
Use the distributive property to multiply -2 by x-3.
x+9+6=0
Combine 3x and -2x to get x.
x+15=0
Add 9 and 6 to get 15.
x=-15
Subtract 15 from both sides. Anything subtracted from zero gives its negation.