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2x\sqrt{6}-6x+6\sqrt{6}+18=0
Use the distributive property to multiply x by 2\sqrt{6}-6.
2x\sqrt{6}-6x+18=-6\sqrt{6}
Subtract 6\sqrt{6} from both sides. Anything subtracted from zero gives its negation.
2x\sqrt{6}-6x=-6\sqrt{6}-18
Subtract 18 from both sides.
\left(2\sqrt{6}-6\right)x=-6\sqrt{6}-18
Combine all terms containing x.
\frac{\left(2\sqrt{6}-6\right)x}{2\sqrt{6}-6}=\frac{-6\sqrt{6}-18}{2\sqrt{6}-6}
Divide both sides by 2\sqrt{6}-6.
x=\frac{-6\sqrt{6}-18}{2\sqrt{6}-6}
Dividing by 2\sqrt{6}-6 undoes the multiplication by 2\sqrt{6}-6.
x=6\sqrt{6}+15
Divide -6\sqrt{6}-18 by 2\sqrt{6}-6.